{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44394,"title":"How to calculate the length of a triangle's side given two angles and one side","description":"You are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\r\n\r\nWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\r\n\r\nThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.","description_html":"\u003cp\u003eYou are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\u003c/p\u003e\u003cp\u003eWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\u003c/p\u003e\u003cp\u003eThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.\u003c/p\u003e","function_template":"function a = triangles(alpha,beta,c) \r\n    \r\nend","test_suite":"%%\r\nalpha = 30;\r\nbeta=40;\r\nc=1;\r\na_correct = 0.5300;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 1;\r\nbeta=70;\r\nc=0.5;\r\na_correct = 0.0100;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 40;\r\nbeta=100;\r\nc=0.2;\r\na_correct = 0.200;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 1;\r\nbeta=1;\r\nc=11;\r\na_correct = 5.5;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 37;\r\nbeta=62;\r\nc=3;\r\na_correct = 1.8300;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":4,"created_by":157578,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":133,"test_suite_updated_at":"2017-11-02T14:53:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-01T17:15:24.000Z","updated_at":"2026-03-30T19:14:20.000Z","published_at":"2017-11-02T14:10:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47295,"title":"Find Logic 13","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 102\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 99\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 103\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\nassert(isequal(logic(x),102))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),103))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),97))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:07:30.000Z","updated_at":"2026-02-14T07:02:11.000Z","published_at":"2020-11-05T07:07:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 99\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 103\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47370,"title":"Find Logic 25","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(11) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(15) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(22) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic in problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 6;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":234,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T13:48:01.000Z","updated_at":"2026-02-14T13:45:20.000Z","published_at":"2020-11-06T13:48:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(11) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(15) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(22) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic in problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47345,"title":"Find Logic 20","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 7;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 7;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),9))\r\n\r\n%%\r\nx = 6;\r\nassert(isequal(logic(x),2))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":365,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T05:30:27.000Z","updated_at":"2026-03-17T20:15:27.000Z","published_at":"2020-11-06T05:30:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43301,"title":"Calculate inverse matrix in m by n matrix ","description":"  x=(1:10)'\r\n  y=roundn(2*x+7*rand(size(x)),-1)\r\n\r\na*x=y\r\n\r\nEstimate a using inverse matrix calculation. This is principle of linear regression.","description_html":"\u003cpre class=\"language-matlab\"\u003ex=(1:10)'\r\ny=roundn(2*x+7*rand(size(x)),-1)\r\n\u003c/pre\u003e\u003cp\u003ea*x=y\u003c/p\u003e\u003cp\u003eEstimate a using inverse matrix calculation. This is principle of linear regression.\u003c/p\u003e","function_template":"function a = reginv(x,y)\r\n  a =\r\nend","test_suite":"%%\r\n  x=(1:10)'\r\n  y=3*x\r\n  a=3\r\n\r\nassert(abs(reginv(x,y)-a)\u003c0.001)\r\n\r\n%%\r\n  x=(1:10)'\r\n  y=3*x+2\r\n  a=3.2857\r\n\r\nassert(abs(reginv(x,y)-a)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2018-07-19T15:35:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T09:36:59.000Z","updated_at":"2026-01-02T15:53:13.000Z","published_at":"2016-10-10T09:36:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=(1:10)'\\ny=roundn(2*x+7*rand(size(x)),-1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea*x=y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEstimate a using inverse matrix calculation. This is principle of linear regression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43334,"title":"Solve the system of linear equations","description":"  4x - 2y  +6z=8\r\n  \r\n  2x + 8y  +2z=4\r\n  \r\n  6x + 10y +3z=0\r\n\r\nInput is each coefficient of polynomial. For example,\r\n\r\n  a=[4 -2 6 8;2 8 2 4;6 10 3 0]\r\n\r\nFind x,y,z. Output should be\r\n\r\n b=[x;y;z]\r\n\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003e4x - 2y  +6z=8\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e2x + 8y  +2z=4\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e6x + 10y +3z=0\r\n\u003c/pre\u003e\u003cp\u003eInput is each coefficient of polynomial. For example,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ea=[4 -2 6 8;2 8 2 4;6 10 3 0]\r\n\u003c/pre\u003e\u003cp\u003eFind x,y,z. Output should be\u003c/p\u003e\u003cpre\u003e b=[x;y;z]\u003c/pre\u003e","function_template":"function b = solvepol(a)\r\n  b=\r\nend","test_suite":"%%\r\nx=[4 -2 6 8;2 8 2 4;6 10 3 0];\r\ny_correct = [   -1.8049\r\n                 0.2927\r\n                 2.6341];\r\nassert(abs(sum(solvepol(x)-y_correct))\u003c0.01)\r\n\r\n%%\r\nx=[     9    10     3    10\r\n       10     7     6     2\r\n        2     1    10    10];\r\ny_correct = [ -2.6456\r\n               3.0127\r\n               1.2278];\r\nassert(abs(sum(solvepol(x)-y_correct))\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":"2016-10-15T04:33:08.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-11T14:18:34.000Z","updated_at":"2026-04-01T07:49:35.000Z","published_at":"2016-10-11T14:18:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[4x - 2y  +6z=8\\n\\n2x + 8y  +2z=4\\n\\n6x + 10y +3z=0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput is each coefficient of polynomial. For example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a=[4 -2 6 8;2 8 2 4;6 10 3 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind x,y,z. Output should be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ b=[x;y;z]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47240,"title":"Find Logic 6","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 212.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 106.31px; transform-origin: 174px 106.31px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic and Make a function by finding logic from this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 29\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 66\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFunction logic(x) will return 'x' th term of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 3;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 3;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 66;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 514;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":402,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T06:26:21.000Z","updated_at":"2026-02-27T04:52:00.000Z","published_at":"2020-11-04T06:26:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic and Make a function by finding logic from this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 29\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 66\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFunction logic(x) will return 'x' th term of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47350,"title":"Find Logic 21","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 72\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value equal  to 'x'th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 45;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 72;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":261,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T06:12:12.000Z","updated_at":"2026-03-17T20:16:52.000Z","published_at":"2020-11-06T06:12:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 72\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value equal  to 'x'th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52824,"title":"Easy Sequences 31: N-N's Sequence","description":"We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number  appears  times. The first few elements of this sequence are as follows:\r\n                        \r\nAs you can see,  appears  times,  appears  times,  appears  times, etc...\r\nWrite a function that output the number  occuping the  position.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times. The first few elements of this sequence are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABAwAAAAlCAYAAADGD3ubAAAN4ElEQVR4nO2dYXHrOhBGPw5hEAIhEARBEAZlEAalEAyBEA6lUAyl0PvD3vFakSzF2t00vt+Z8bx5vamV49qydrWWAUIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEkBB2AE4ALgDOL/4uhBBCCCGEEEIIyXPGELufMMTybuwAXAH8jv89ATh4NkgIIYQQQgghhJDV7DHE7jqWN08c7AB8jQ2wqoAQQgghhBBCCHkvzhhi+i/rHX9gykasZQ/nEoixjeO4ebcF1VZEpcVOtRfBYWxrH9BWtFuu7YjzBRiOa1Rlzpbc5HzMbVfYnqf6fEy3E4BPw7YAunmxw1SCdx//63ktHMY2rpiq8Lygmx3WbkvXWG7rdVu6xtKtt3+mG93WoF29xyPaNWKsRTcb6BbPDQ6FAJdxp5cVv7vHVP7gdaBOAL7HNvR2h/2AVD+aobcfDIkVa06Yqjv09gn7k1zcfpK2vuETzEe6lZD2Iy7i09jWLaAtYDtuOzyek+l1bon0d6XN8lqgmz1HTDfCO3yr4nYYjqncfy7wTYLQzQZPN5m5adl+DNrNjX1KW29CkG50a0XG/j8Yrq+L+n+PsfkZwzG9qfa+4DM2p5sddHsdPbG96U5zgbVH4PKJmM4P436WBsAWHbtGOnmZZfnE/CZjOeCWx05+xnYumAZvHsFEpFsJHTx5B9U6eIpIGGzJbctBLt1s0fcD78fnDpj6LI/BRgrdbPB2yyXBva45SdS2br3XHN3o1sIBUxCWTv7Iv1mOzSXWyFUHyb9Zjc3pRrcWIt3W8icSBvIWhXQG2TpwOY771aWtUs6og0+rZzTu4371gOaAx8SIRbnmcWxr6WSzHHTfkV8AQy4ky4Ai2q30HfTfzDuovqu2vBMGW3KTIDcqGyuzjhEVLnSzbU/uNV4VURo9Y+ddEUU3O7zdpO+tJT0+Gz9X44560mOH6fj2QDe6tSLj79JY2OIxZ6HlWWwZw1oEg3SjW41ot7X8iYRB7nc9ApcvlP+46Wxab9uncX+l/WhPi6DpvtDWXrVlMSCXUtASEsT/GLQFxLrlkHNDV1B4BtUSqMnA2DNhsDW3D9hmfWtIhU0EdLNDJ608n68H5gm53GyFNXSzIcLtirb71jf6r4892hKAMnjtvfbpRrcWDqiPPeRatBhTylhnaewh/UzvmJJudGsh0q2H/yZhIGWFS52uLnPs/aPcKvuQbLDFCSdVEktYDrJOWL5JyN/QolIj2i3HDcPFqgeQnov1SbWEdBCeCYOtuUkyImJhGhmgfSBm3Qe62aDvMd4JEZ2IjkiI0M2GKLeW2VnpN3sr9mSR5xoyeO2t3qAb3VrQY4/SGE4+01s9AUxjj6XxqXymt3qCbnRrIdKth/8mYXBCPQmgT5LehEHLit5yAljNxJeQWfio8mKpMIjIhHm7fYz7lpu2Z1C9G9uS68Y7YbA1t9xCTV/jzz3OjXQRqh8M577H8aObDboiKSLI1Y9MeQe5dLMj0q2GTGSYDtIKyETGD2LGCnSz4Z3d9OTZF/LfX9qzuBZr65/oY9nbz9CNbi1EuvXw3yQMWtBBk/ezkcAUNHkv2CfH1LuEE5hmZiLKUwFfN1mPQc4F76D6ivm54Jkw2KLb0irS2tWC2irSufU9eqCbDfrGLI+neb2mVQ86fjHd6L1eQUs3G6Ldasj1EdGuXPsWz+W2QDcb3t1NJ+jSsaOMVWRyoxedfMyNHeW7WAVFdKNbjWi3tTBhoJBON2omXjpdz5n4M4YTOypZ8IUhCIw4ft5uX5hnDz2DannVp96vZ8Jgq27Hsb30LRqljrgHqcz4wOMbQnI3mV7o1o9ep+YT82fiZbvBZhAgiyLJPeWStC8/t+r/6faebktI6bfVQsw15FqPGC/QzY53d9OLmepEsawFZp2kTpPiUhF8Q3mB7bXQzQ66vRaXhIFkQ9Y8a/HKhEFkFkeX0ntkoA+YD/Q9VyCXdQb0oMrz1VoRbp94LEXyCqrl9Zvp9eIVVG/ZLSU9Lz1LNqVz152+Z19Ct+fQCxnpoE9mqfWMgkXpX3q8rhhu+kc8vpmnt6yRbu/pVoNl7TbQzQ4vtzRAEyevQClXSec12UU3O+j2OizfDAFgChDWdl6vShhIKX1UdYF4egTxMgOTm6mzHuAcMS2cl7bl8bxNhNsR+TdceAXVd+QvQI+gestuJdJO33sQpzt970Ec3drR7zIv9fPar3cGTX/3XD+f+vUMQuj2nm41WNZuA93s8HQrBWhesUAuQPN6NSzd7KDba5A42WTsJ6UaafnxM7wqYSDtRqxdoJ/z9yY3M+h5XNOZQc+A0MNt6X3wHkH10rvurYPqLbvVkETmL2KuO/3MtXefQrc2WlfZ14ODHr+WxKkOhnv86PaebkuwrN0Outng7SbX+iceHwOy9jtg8LjjccLLYw0uutlAt9cibxxc/ZiEzoj0ZjlfkTCQTjDqdRU3lFfe9EIP8r1nIfUgP6JMztLthnIQax1Uy3lX2pd1UL1ltxakdNn7rSTAfBGbiGed6VZH31uWvrf+XE9/ogPP1s+t7Svp9p5uS7Cs3Qa62eHpJv28BCF7PAZNVglqWbROB2EfeHys1gq62UC3v4M+DqtiZ1nc7J0qDOR1b1GvTpJX2UWvz6BXfo4I0nQQ7+1q5SYXpzyvmm56Mayz+vmaG7Wcd9dCW0dMM2Z39bO1x3LLbq3IrGBEUA1MjhFBNd3q6HN86Xvr5FlPf6KTpkvoG2/P9U2393NbgmXtNtDNDi83Gffnrlu9Rsm3QVtSaZm7bg+YB2gWk4h0o1uNaLceuisMNO+0hoE8mxKVLJAFk6KTBULkrK7nqvs5LNxy6zC0bGv89PF5Zlvrt2W3Z7+XRQffghzziA6ebu37+cXyDJlV4CnHqHYvtAg86faebiXEJaqsXVwiytrpZsdW3CQgKnnoR097Z3QlAVny0IusWszo0o1uNaLd1mK6hoEg2Zc1s09RCYP/LVkATDeXiFlBublEzXhauMmCiqVNPyOrnzNak20/VNq6Yz7TJT9bWwq4ZbdWZKY6ajZGjmnETBPd6rRWIrUGqDVaq6xaA9Ql6PaebiVe8camqLJ2utmwFbeWySUdMPWOX1smlyQY7B2/0o1uLUS69SAVTaZxc8+7GqMSBi3JAqusbe499CkH+A++v+Hz5oIcLifWAhFu71g10cqW3YT0eTRPZDAXNdNEtzbkprtUraDX5OlpUw8olioxpMy393jS7T3dckhCNeJebf6qrAp0s2Erbq1jj8jgTOKQiMAToFsLdHt9wqAntnfZ6TMJg+P4+TOey7BeUS/rOGPeEe8wnBSXhu+lkedPlkpWpNpBd8Rr3UrIBZAL4Ne6LXFHOUnyrm4tnYilW60Todv880eUBzMS5Jau+2fdDli+piXIzX2GbvPPR7rp1e1LQaXMMKfB6ZrrTSoxSkGlnj1Pg1O6TWzZLUVcWx7BsbgHiGvL40V0K0O3gTVukowouejrLb1XPOsmiZYlF+lL0mQM3ebQ7fVuur3cOErcSx5Lv5vytgkDvVL3MzOVMtj9HNvKbbkBsV7koiWZAUzJgq+Fti4YThI9IH7WTb+VIPe+ztzqm5pn3fTALBc0LM0I/nW3JWpB9dpzskQtqKbbhF4U5oL5uSAJua/Cfp5104uw5ZJiMtNZ6v/oNhHpJsi5l3tTjV58KO3b1lxv+rrK3bDlfpcmROj2yJbdct+3pTqv9x6gy9prA0a6LUO3+WefcZPrqfT2MLkvpd99jZvuK3LXtizanPvudJtDt9e76fZyjydp93TcVvvdlD+VMNhjOii139dlg7LVOs70pFna0pmFW/LvtTKwdGXL2nZKfvcZt/QE/cGUELliOKZLJTPPuqXHUZ4/v2A4bje0PffzF92WqAXVa87JJWpBNd0e9yfbN4ZzRN6de0W5M3zWLbeo43VsTyprlkqi6fYaN2Gn2r1jOt/3GPoveZtIytrr7Yz5YEC/MkmugVwilG5ztuymKSU+cvTeA8SlVnEJ0K0G3QbWuslEVJogljc8WV5vstL777h/2a+8Ns+6L6Hb43ek2+PvrXHT7eUSiNo9TfjVfjflTyQM9igvynZFOSCUQWzLAlynwv5LW5rlOWA48PKHq51w8tmWLXfSPeMGDB35NdnnBW3Pcj7rJiUu2uFz/FlrWctfdavtS75D6Ts/67aEXBOl64huc86YX3cS6Hqck7k+S0rQatBtTqSb5oi5p9xrlhIUa6836TO15wXLA3C65dmym/TDrbPAvfcAOY6taz7QLQ/d5p9f67bH9F0jrrcz5mNLz76EbnPoludZN2DoB27I9we7cR+5Cu3a76b8iYRBL0fEvU4MyCcUvKCbHXSzgW520M0GutlBNxvoZgfdbKCbHXSzgW7vwyYSBjfEvCoQmMpGIl5jA9DNCrrZQTcb6GYH3Wygmx10s4FudtDNBrrZQbf34e0TBlJqEcEB5QW4PKCbDXSzg2420M0OutlANzvoZgPd7KCbDXSzg27vhUtsf8a6hVzWtBNVWrLD8MePeL8uQDcr6GYH3Wygmx10s4FudtDNBrrZQTcb6GYH3d4PWUDR1E1eh/WL9kVZCCGEEEIIIYQQ8jeQQoDSaya7kJUZpdLgiLjsDiGEEEIIIYQQQp7jgGHSX8fyrus/7DFkJlpfy0UIIYQQQgghhJB4JHY/IW6hSEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGE/N/8A176kSy3idycAAAAAElFTkSuQmCC\" style=\"width: 518px; height: 18.5px;\" width=\"518\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs you can see, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, etc...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that output the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e occuping the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 26.5px; height: 18px;\" width=\"26.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = nnPos(k)\r\n    n = k;\r\nend","test_suite":"%%\r\nk = 1;\r\nn_correct = 1;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 20;\r\nn_correct = 6;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 1000;\r\nn_correct = 45;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nks = 12345:12345:246900;\r\nns_correct = [157 222 272 314 351 385 416 444 471 497 521 544 567 588 609 629 648 667 685 703];\r\nassert(isequal(nnPos(ks),ns_correct))\r\n%%\r\nk = 2000000;\r\nn_correct = 2000;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 123456789;\r\nn_correct = 15713;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax;\r\nn_correct = 65536;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax('int64');\r\nn_correct = 4294967296;\r\nassert(isequal(nnPos(k),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-28T18:15:10.000Z","updated_at":"2025-12-22T17:00:59.000Z","published_at":"2021-09-28T18:16:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times. The first few elements of this sequence are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left \\\\{ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8 ...\\\\right \\\\} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you can see, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, etc...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that output the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e occuping the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\\\mbox{-}th\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52779,"title":"Easy Sequences 25: Product of Series","description":"The function 'P(n)' is defined as the series product:\r\n                            \r\nwhere 'T(n)' is the triangular sum:\r\n                            \r\nIt can be proven that P(n) is convergent, with:\r\n                            \r\nWrite a function that outputs the integer value of 'n' when '3 - P(n)' first becomes less than or equal to a given tolerance 't'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function 'P(n)' is defined as the series product:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"124.5\" height=\"46\" style=\"width: 124.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ewhere 'T(n)' is the triangular sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"184\" height=\"19\" style=\"width: 184px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be proven that P(n) is convergent, with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 30px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKcAAAA6CAYAAADV7klxAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAp6ADAAQAAAABAAAAOgAAAAAcyFpzAAALKklEQVR4Ae2be7BXVRXHr2CIgYQCPgj1qvmgnOKhGQoykPhMDSxzLo0VZPnoNWr+UQimMqGjaZRGps34QJxQ0DKFFIeHXi0RK3WcQLz4wMBXiBAJQn0/957FLHfnd36/83vI796718z37rXX2nudfdZZe+29z+/choZI0QPRA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QMVeKBJfV8UdqvAhu86XpVm4QAvjHz0QF4PXKAO24SJeTtmtN9Zuj8KrwsHZbRrL6rhGuiFwq+FycIYoVoTWaY6BvHA1xXAvyR/XrhfmC6cIRSjo9RgszC1WMMy9D3VZ5nwtNC9jP710OXjGgT+/G8KVkt2uFAR7aTeQwQinqWmvxDSNAmWCueFijqsD9SYCETvMMY/QSDIyFamu1f8XkIa7S7hKmGugI9qQfh6jXBLLYzX2OZHZZ+JhS+fEmYnpfmW8m2ht5CbeqnH3cKbgjd4YGCJlG36/4jvGujrsbrEjfmBYIAfU32l088P9FYlcLcItV52v6dr4F8mT3ui6zXYTcKZwaDZRz8nWMyMC/QlV0er5SXCVsGMhcF5hNOtEt9FqGf6iAa3QbD7Yc8Y0tkSmP498T2DBhyA0P8mkNeiypLOEsiYw3HU4nrVsElie1cYW8DYlyU3/15ToE3J4uXOWBicGOFiLImfpFLn5DM9DkrLfH7C0eak4J4WqI68MZDXqnqRDHO9CbW6QJXtDpK9KzJsHisd9wO+m9GuJNXDiSGMpQVnSUbqpBFOM8esKDCm010b2o5y7fYVz0ryrJPVmmWfzDgW1/pCH5L9Scn94EfuLZV4ZVEK4ZiOQie6G5nneM8e4yrrxHMQNBovpotA9iyF+qrR4ARMBg5Q0P7CqQKZ+34hyx5vETgYjRA+IbwgtFdiW2X7TBIF91YRPaTeBCjIypyFTrZ28b3FdLWKSh4yD8nLnLqVHaC/7LuqQf1khNlq93JyilFm8lrXho29p0Wq0P80L0zhr5XsVcGuRUlgQ98QNghedySKDLpTOtqfk9Gm3lWc4DmAch9TqjXYrODso4ucJzwqbBN6CJ4aVWFf8ZjAoA4VhgmPCBsFZG8IMwQLUvaus4TVAvrNwj0CN1cJ2UEGm7xZ8PZ2Up3lmwyFHjwhhBOjJdGRwbKI++SkytixtUXg9ROn7/eF64QHBbsWPsyiyVLS9vKsRgV0cyR/qwr4fAH7xcQkoZOEZYLd73rx+KJiSgvOXWX1D4I53y7qg/Mq6U1uJQ+F7AVeFHhopvuBeFI+Jz1OycsFr79Z9UroNnW2axGcZCNAkKwSTMf1fyoQTJ4IYMZFu1Dn2xnPEoYt2jMZxwr/Fo4XoO8Lds0TWyWF//BWgba/LdykoMY/P7teOWWxMaYNgASwUih0PXyQSji7FOLmjksaHqSSoIKOFRqFWwUjXneQESGyDvVm4WDB6CdiWPZ4cEcLZFWjbWIuFn4lEEBDhMeFbgJL4d6C2RdbMnGv/xRs6/GseCYWk4zrvJQAR84U3hZC2lOCtQITi8DD4VmEfxYlDX6ucoJwvnBHIrslkVHtLzC+QnSWFLMEnoUFd6G2oZyMx3OrlObKAKtcXtpHHXoLrDYkoNGC0TtiiI1y7Lba8DPvQLPqyjXibWb4zGlN7nL6c0zoyhanv9TJjb3P6YeaMGc52NlgrINy9qf5ZwT6vkmlBLpSbcwvBP9NQZ9/JHomSjEia2HryWIN61xPkjhXsBWFe2pKG3OXNGEZsmJRv87Z5CGF9JQTPON4Y1uMUWmZz4lKYnm4RmS/v1klR0nmhrq3FUX/+gzHdoCsYbSfmEOSynwTZpRkeIj9ansmgnGGcIO7icMcv52tVnBywUro5SKdmWVGvY3JWfrgtJUgp4nWAxp9WB12KdK5j/RDXZtzxbPfNPKB+ycTZpTYg15tK9r933nuDnZ3/HZ25+3cjmUqDe5io++lBsNco1KCwTXfzrI3ZZXoJxAsrwmF6DgpbPJzvUeChmOSOjYXB7q0at9EWE5wzlHfkWlGc8p4+7AgZ59CzZul4HyBj1akNaqX4EwbWzVlo2WMA4wRmbNcIjgIzv5CVnD6zHh9cDEeiL2WWSJ+U6BPq+6TCMsJzt3Ud480ozll3oc5u/5fc1ZA/AA901Z88G9nCU6/pHP4WPNBN+SqPa/WHK5GCEszelpwkmnDyUB/W6Yti3Nyv11YKKQRJ3+onL3yNPWb3dq7sj/+bFCZpYaGUxIDf1W5MM1YZwhOZudp7uabHV8OO1OdmgSy8XUFDAyUnF+2oHuF8BBDYBuxTE4VCL4LTRiULOm8KXhNCLcHQdPUKtcAHxYx8a4S2Jf/Uviz4ImV5wphq/BDIXVbV2pwcvzPIkvPtCnWNstOtXVdZXCKYEsi9g8ReggbqZRBnKx5H0kw4b8w8CRqOIE/Cf3eGFeyJTCaLubTwgjhHRMG5SjV8eudwrZAV4/VL2pQE5OBjVc5S7haYBU5WviZwIT7ivCwUBH9Rb2JbvCpFEsvOb0PBGt6m9P7LGb6G5z+bBO68hqn/7aTZ7EHSLnB9bPxU24WviWUS2QF7KSNFZu/S/RMgF0RBHSy6gQZNlYLPLAs4gHSliBuD9RLg3xFYMwe3PNK4UZhgFAxDZeFLYJd5DLxzGIjZrzpKC8yRVKy8W0RrM3NgZ6Ht8zp54j3GZ3NvNfPVr2aG3OZy02N6kGWe0HwY1W1ZGKSDxPSgtcbGakKviPg2xN112BZQSYIXxOOFHoIVSGclhb9OIpfSL4ukDEtAyA3rBXPHon9Rlr2IluMEiYL6wXrZyX2vyqwNPBu0ORWviHZl4QdSWfo4oznmzUexGLZZxKQjSJFD5TsgWvV8l1hUMk98jW8VM3fE4bm6xZbRw+0LelL5AhWggFVdggHCTLzd6psN5rrRB7oq3ttFnj/2LVK932M7PDL0ZQq2YtmOrEHuune2QP7V2qVuONQdS52gq/EfuwbPRA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QPRA9sIM9wJdH/oubXSoYT78K+sau0QOtHuCnOL7uXiisE/j3Bj7tekLg66NZQl7ik7cWodgvHnwH+gthqcDv1ZcI/PJi1EcMH1rwU+FDQvzNWU7oTMR3kkcJ/K7L1zZDBP5nZpLAN518ylYO8c0nn7l9rkDnfSXHNoH5gMC1+OhhkcA3gHy+95yAzOMm1av1k6FMRap3D+ynARIAZCc+ZuB3XrLfVoGMVi4R4JsEyvBj4QclWyhYoBHEBCvjmCsQhK8ITQLjOUsg2NEzmSJ1Eg/w8SwP/X1hXHLPJySyy5M6BUs82bVUYA+7gCw4QID4kocPiidScTRc/GaB9huEwwRPZ6qC7kdeGPmO4wF/4LG7Oj5hyJz8ywQ0pq1omJ+UFI8LfMVeKn1WDfkol4C7W3hdgA4WWLb3oOLoUfFThcsEgnON4Ilsi63DvTDyHdcDLKtvCXx9vb+7zb+L54CUFsyuWUGWk/89wpPCwKAVJ3kOWxx0QuIzNLIjuCNUqr5KmJYij6IO6AGyG4FgGZNb3MvJ9hT/BYQ56Uq1f0xg75pG9g9sk6TsKXAIOl/gYDZd2Cgwrh8LRoPFIDvCBLHs2B4gOHjgTe42xyYye8XEP67lod5qfJ9QKDCxdYHAdQEHLzIp/AwBOl1AjmyewN73ZeFGIVIn8cAC3SevcQgoo5FiCApOx6easAblONlcIbClWC4wUboJRqPFzBTWC08LFwuRogcaGuWDcveb0X3RA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QPRA9ED0QPRAx3CA/8DP/7FueXvY8cAAAAASUVORK5CYII=\" width=\"83.5\" height=\"29\" style=\"width: 83.5px; height: 29px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003efirst\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e becomes less than or equal to a given tolerance 't'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(t)\r\n    n = N(t); \r\nend","test_suite":"%%\r\nt = 1;\r\nn_correct = 4;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.5;\r\nn_correct = 10;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.01;\r\nn_correct = 598;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.007;\r\nn_correct = 856;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.00032;\r\nn_correct = 18748;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nts = 10.^[-1:-1:-8]*3;\r\nns = arrayfun(@(t) N(t),ts); \r\nss_correct = 222222205;\r\nassert(isequal(sum(ns),ss_correct))\r\n%%\r\nt = 0.0000000026;\r\nn_correct = 2307692306;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nfiletext = fileread('n.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-24T21:04:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-24T20:12:14.000Z","updated_at":"2025-12-22T16:55:44.000Z","published_at":"2021-09-24T20:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function 'P(n)' is defined as the series product:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(n)=\\\\prod_{k=2}^{n}\\\\frac{T(k)}{T(k)-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere 'T(n)' is the triangular sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(n) = 1 + 2 + 3 + 4 + ...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be proven that P(n) is convergent, with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lim_{n\\\\rightarrow \\\\infty}P(n) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e becomes less than or equal to a given tolerance 't'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52921,"title":"Easy Sequences 40: Quadratic Congruence","description":"Quadratic Congruence is a modular equation of the form: . \r\nIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (), and a modulus base (). Using these data, create a function that outputs the pair (), which are the 'primitive' solutions to the quadratic congruence.\r\nFor example consider the congruence: ,  the solution is , since:\r\n                                    , and\r\n                                    .\r\nNOTE: A primitive modulus to base , can only have values from  to . This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 235px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117.5px; transform-origin: 407px 117.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eQuadratic Congruence is a modular equation of the form: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 167px; height: 19.5px;\" width=\"167\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297px 8px; transform-origin: 297px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 18.5px;\" width=\"79\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and a modulus base (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eUsing these data, create a function that outputs the pair (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 75px; height: 20px;\" width=\"75\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e), which are the 'primitive' solutions to the quadratic congruence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example consider the congruence: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 157.5px; height: 19.5px;\" width=\"157.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  the solution is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35px; height: 18.5px;\" width=\"35\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, since:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkgAAAAnCAYAAAD0I7cJAAAL+UlEQVR4nO2d7XHqPBCFTw90QANpgApSAR2kAzqgBWqgBHpIC9SQFvL+MOf1oujTXsmS7z4znjs3YJCl1epotRKAYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiG0TWfAB4Afl/XA8DHpiUyDMMwDMPYkDOA79e/nwDumIXSacNyGYZhGEbvHAB8bV2InXLCxsGaJ4Cj8zeKpHv74hiGYRjGEBxgKy41OWDSIefaX3J6/Ss5Abh63v+JSSB91yyUEqfI1YvAO2L8aNwngAumOr1ibIewtuwj1gV9wAl/J0Q5fKCD2ZwSB0wO94JpcLvgr28cjRIfs9YWeoTP39LPHjCNkXvoEy60ES3/Fhun3cu1SdZzNZH0jUnw5D7oCWNEkFjO0HXZrmj/cwTw87pG4wjghqnsT0xh5JEHkhOmAXFJW4xaFx94zy/k9UR6MDlg6kM/mBwlBcUTk0gcDU6amGdZdVbakFwfs8YWeuWMqfx3TPbJPtqif1Jc7wmm3EjbWMsR8XHavXy+5fAqi7oYvYgvzv3w8+v9va+r+jq7bNgeZkcs42gC6YypzL+YBscRxEAId2AobYtR64KR4FJnBMyzNt97KDJ80edeuWJ+5r0II5LjY9bYQq/c4LfDL8wiuFZfvUBHPPQKbeKm8Fmy76WuH4Tb7AvKq1puhCVXIN1eBel5IOCz9RzelOJ0JIFEx7OHweQLUzt8YhY5JW0xal0cMD3nA+/RAXfH6i/8/TyWh8jPHmFQlUJv5EhJiBwfs9YWeoQi6Al/mflcNUQ863Mkf1DCAXo+j3WVmlhSwKcE2RNKUTsWTO5KyxETDIdpOpJSgZbDHX3nSMllyhoCiZ+v/bnS4Y4UIcihNJrXsi602/OK+CRHDoxupFhOrEICiMIxNECVwrrWXtaXz9m7mCsl18essYUekQI91C+5ClJjEr336JGMNq7t22fk9Wn6k1Qf5ZL/au6YZwwlhvKAfifRNlSKuBv6nBFyvfSC2fGPIJCkrfQsPpdSIpBa14V2e/4g3t+kE3QdmBxwQ8vUcgDSEB41BNKexX6Jj1ljCz3C6FHM9mTei3bbMyKyVyhWNPxe7kYA5tClBBnbdVVk6wtzDk6JQLqiTsNrCyS57CE7di8zRIpTYCyB9MR+Z9tAmUBqXRea7cmE8hS+QVGG12Oz5A/xPo08BW2BJAfImNAblVwfs8YWcpC7x9ZcJZEKmUQca1dGmTSjPRSTe/SPhL6vlQhknT5Sb3zBpPxFfGAyDEZWcgXSGVNHqrEGrSmQUhnx39jWGXJXBcswikCSs0jpUJY4sF7JFUhb1EWtJdMYfEa5pi/9RcoJ5QipXLQFkkwMpUCQ29tHpoaP8dlCDjJKt+YqGRuk8I0hlw61xgTaVakPOOLvM/LoDN9nxV4LsfToBopclpF11qqfMOCRGxW6Y4Wtf+Nd+eUIpDP8Gf8H6MwOtSNIdHQUdZwpbD1j5HZbObsYRSDJXLU7/FG6byzrNFvMMn3kCqSadRGitUCSEw3ZL+XyRa5AWjJguGgLJOkTrvDveL1jmZ/Y0p5r+JiQLeTAsWPtldsOcgAvEUhaER9+Zooz/tod/cUH3qNgcuw9OvekghZMtP/GfMwB70vVKYU2733i3de1gstruTZAey/uu75kvJRAktnjF+fSOu9EWyC58LwW6fxyw3WafOOvoBxFILki84LZkV+c10ttYotZpo9cgVSzLkK0FkjMIXL7iWyrEoG0tm00BZIcRH8xn1vFNpSDwJLJ1Jb2XMPHhGyhR+R4ViKQtPJquRswhyPel+qBeYWHyctygsHXrp7XXHiCt+/ZZA5R6F4KNBm1kZHzVrZQurwGzPZeNEE9wZ+MFxNIbJBQB9baoVJbIBH3eVqG0i/wG+QIAknmnYTaya3bErtoPcsMkSOQatdFiNYCiXXhPp8c/FODihyAehJI7hKpr31kknlpMupW9lzLx4RsoUdKloBLbDmX0sGcfuKO2W+wnrlcx+VS32u+NpX+x/dcso7cZavYvfK+VrsZS5fXgLmc2fdw22Oqsmp1AK6Xhi7ZWLH3aSCdY+l6+gfmn48oXfsN1e8a5xWrKy6F/CTel9Pmso1ig4XM6xjxBNkcgVSzLlq1Z045QuWWg0rqueQyQapcMv/Hd9FRPhLvyxEVubvXZPlbTqaWUNPHrOnPrZcbZf9MCRXZR7cQSHLpkpFn2X70Rzx3UEajaZuuCJRHHITKIetI2r+MHPlSZ+TY2Uosly6vAQts9o6wmm4hkHzr+6VXjd1YpbNRGQ7NzeDndttQB1zjvNbWaW4d5M7KSpxTj5QKJO26aNWeMWivodzCWktssr7WXDkDXW7koEQMbkktH5OyhRxaLzduvcRW0t9llPKBvxEPvubmDccOasw511AKHfm5nISEttPLiFYLliyvAYUC6Qtz0l5sZsrKLlXsOTAZLXRJQwi9R/P8DTZ0C4HEAytTM2M3MpBDrE7dJL/QlWNEMmcjd1Ac6WRwkiOQatZFq/aMwe3hof5fsoRR8vz8uZfQxb73k3hfTs6X9HmxgbHkWbeklo9J2UIOWyw3LhFIWsGBkgFdtot7j7Q9V5BIgXMM3BOzVxk5Y3+R94b6RCy6VIMly2tA4VELS6M3LdebW38nZzWlDb1kiW1J3WuICxq8llCRg3PO+0q+d7RdbDXrIoR2e/q4IT0gymWBXIGkcaCcZg6SHAxignKpQGptzzV8TI4t9IoU0zFkf9fa1fxEvkCK5Sn6RIz7miucbpF7JHKy5bvXVxdyYlgqWJbApcI1mySyAg2p6I2sLBnBabkNvrVAooG1aOjUzEhGpTSjZdoDKu1ESzxIRtvFVrMuQtQWSCUDYs4AFMpzWIqmQJJLFLnLpCWRudb2rO1jRhZHwPtgH6tDTQFP6ENSpA5SpY/xlS0UyZHtnBMBlv0yVReyTlvYxRnLfSf7n0o5W+QgpWj9/U/0c3ruCLvYgPdliVC9LT2+f4swvI9cgVSzLkLUFEicRMUcioxoSAEQen5ZRxr9WvscJOZqxPIp6KRTM3LffT3YMynxMaW20CNyTAtNgqVA0dyRlXsGj4wQuf1DCni3bPI11yZzBJ/8mSC2oawLn6+S9dnqJ6ZYziVBDE4KVNibQGJ4O9SB6fR6SbocRSDJjhka8ENr46OQK5C2qItaAumM91OXffDgOiJ3yoT6UWiXzVK0BZJsn5D4aZ2UWotcH7PEFlJstXzOvhyKQMi21RR7FBspQc3+4bMtKczdtnB/KJa5e8DcJ0PtE9qFFov2MlHfff0L9bb6S/+6xHf+QDFPak8CyT1F1VWfPOPhjn5mQKMIJCAdOaBT6kV8lpIrkID2dVGjPemI7/h7CCyv6+s73eegs/UNMCfxmnYURDNZmm3kOztIisDcTRO9kuNj1thCznevvUrHBp4bFIrQ1GzbJ+IDtLu934XRE5/QueDdZmUf4zKYr0/K841iESvZFyiG3Xyoc6BsWtAWl3wHfY9au+5JIEnD5/XA+xHrrQ64ymUkgQS8H1BGI+RPzowsjmQ/yO1gLetCuz3lLDV1hZajZZ4AXz+93v+Erj+pIZDkacMPzOU9YnLO7k92jErKx2jYQogtlxspCuT5QmzbnCjPUnimUWoVIzTmcQzzRaflJM49N0lGey7i+8+v98Z+h1TmGDHR/Bfzznb5WugEbi0oEJf4zxuUI75ye+1WyyKaAu2ASQTJznV9/a2XqJGEDkR7G3HNnJUjJuOVCZ8XjLmsxm3QPqd8RdqJtqoLzfbk7znlXrEcKvf5b5hsWruv1RBI5IT3zSw39OsvlhDzMZq20CMcD3hkwf31/5q+ihP1UP4M+4svyiTHY994yLa8wf8MvvHvEvgsF3nf1fn8G6a6W5ITVMpSPcJ638Ok5g2GcEccYHuFA9eoER3jnX+9PU+Ynr2FgzaMtXwiHkUy9OEkxzAMwzCMjrmh3aGK/zpc2jdBahiGYRgD8IBFPWvD3KsRfkzZMAzDMIwXzMsz9OFGCxNHhmEYhjEgu0sc7oTeDy01DMMwDMMwDMMwDMMwDMMwDMMwDMMwDMMwDMMwDMMwDMPYN/8BR9r1r/DhafsAAAAASUVORK5CYII=\" style=\"width: 292px; height: 19.5px;\" width=\"292\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 292px; height: 19.5px;\" width=\"292\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA primitive modulus to base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, can only have values from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e0\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38.5px; height: 18px;\" width=\"38.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xs = quadCong(cs,m)\r\n    xs = cs;\r\nend","test_suite":"%%\r\ncs = [1,5,6]; m = 3;\r\nxs_correct = [0,1];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [1,5,6]; m = 7;\r\nxs_correct = [4,5];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [6,-7,-5]; m = 11;\r\nxs_correct = [5,9];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [35,76,33]; ms = setdiff(primes(10000),primes(100));\r\nys = arrayfun(@(m) sum(quadCong(cs,m)),ms);\r\nss = [sum(ys) floor([mean(ys) mode(ys) median(ys) std(ys)])];\r\nss_correct = [5752615 4777 57 4151 3465];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\ncs = [10,-131,391]; m = 6373;\r\nxs_correct = [3195,5103];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [253,-1420,672]; m = 30103;\r\nxs_correct = [3927,8215];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [528,26711,283500]; m = 198733;\r\nxs_correct = [37227,174629];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [4545,13092,-69741]; m = 1000121;\r\nxs_correct = [821876,933449];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\nfiletext = fileread('quadCong.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-10-17T05:04:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-12T12:11:53.000Z","updated_at":"2025-11-28T12:16:40.000Z","published_at":"2021-10-16T17:40:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eQuadratic Congruence is a modular equation of the form: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eax^{2}+bx+c\\\\equiv 0\\\\  (mod\\\\  m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs =\\\\left[ a,b,c\\\\right]  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and a modulus base (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUsing these data, create a function that outputs the pair (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs=[x_{1},x_{2}]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e), which are the 'primitive' solutions to the quadratic congruence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example consider the congruence: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^{2}+5x+6\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  the solution is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4,5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4^{2}+5\\\\cdot 4+6= 16+20+6= 42\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5^{2}+5\\\\cdot 5+6= 25+25+6= 56\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eA primitive modulus to base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, can only have values from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47385,"title":"Find Logic 28","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 21\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 38\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 33\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 69\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will written 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 21;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 21;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 22;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 38;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 33;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":200,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T17:21:56.000Z","updated_at":"2026-02-19T09:52:52.000Z","published_at":"2020-11-06T17:21:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 21\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 38\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 33\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 69\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will written 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43235,"title":"Calculate geostrophic current","description":"  eta0=0.01;\r\n  R=300;\r\n  f=0.01;\r\n  g=9.81;\r\n  x=-500:50:500;\r\n  y=-500:50:500;\r\n  [x y]=meshgrid(x,y);\r\n  eta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n\r\neta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\r\n\r\nhttps://en.wikipedia.org/wiki/Geostrophic_current\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003eeta0=0.01;\r\nR=300;\r\nf=0.01;\r\ng=9.81;\r\nx=-500:50:500;\r\ny=-500:50:500;\r\n[x y]=meshgrid(x,y);\r\neta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n\u003c/pre\u003e\u003cp\u003eeta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\u003c/p\u003e\u003cp\u003ehttps://en.wikipedia.org/wiki/Geostrophic_current\u003c/p\u003e","function_template":"function [u,v] = your_fcn_name(x)\r\n  eta0=0.01;\r\n  R=300;\r\n  f=0.01;\r\n  g=9.81;\r\n  x=-500:50:500;\r\n  y=-500:50:500;\r\n  [x y]=meshgrid(x,y);\r\n  eta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n  \r\n  u=\r\n  v=\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\neta0=0.01;\r\nR=300;\r\nf=0.01;\r\ng=9.81;\r\nx=-500:50:500;\r\ny=-500:50:500;\r\n[x y]=meshgrid(x,y);\r\nvi=(g*eta0)/f*(-2*x/R^2).*exp(-(x.^2+y.^2)/R^2);\r\nui=-(g*eta0)/f*(-2*y/R^2).*exp(-(x.^2+y.^2)/R^2);\r\n[u,v]=your_fcn_name(x)\r\nassert(isequal(u,ui)\u0026isequal(v,vi))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T16:11:31.000Z","updated_at":"2025-12-08T12:29:58.000Z","published_at":"2016-10-08T16:11:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[eta0=0.01;\\nR=300;\\nf=0.01;\\ng=9.81;\\nx=-500:50:500;\\ny=-500:50:500;\\n[x y]=meshgrid(x,y);\\neta=eta0*exp(-(x.^2+y.^2)/R^2);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Geostrophic_current\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Geostrophic_current\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47320,"title":"Find Logic 17","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 281.524px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 140.762px; transform-origin: 174px 140.762px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,1) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,4) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a Function logic(a,b) which will return value according to problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = 3;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 1;\r\ny_correct = 3;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ny_correct = 5;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ny_correct = 11;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 5;\r\ny_correct = 23;\r\nassert(isequal(logic(a,b),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":2,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":457,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T15:48:34.000Z","updated_at":"2026-02-14T06:58:04.000Z","published_at":"2020-11-05T15:48:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,1) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,4) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a Function logic(a,b) which will return value according to problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43290,"title":"Calculate numerical integration.","description":"  x=0:0.01:1\r\n  y=@(x)x.^2\r\n\r\nUsing given two inputs(x and y), conduct numerical integration in x.\r\n\r\n(hint: trapz)","description_html":"\u003cpre class=\"language-matlab\"\u003ex=0:0.01:1\r\ny=@(x)x.^2\r\n\u003c/pre\u003e\u003cp\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/p\u003e\u003cp\u003e(hint: trapz)\u003c/p\u003e","function_template":"function z = integralx2(x,y)\r\n  z=\r\nend","test_suite":"%%\r\nx=0:0.01:1;\r\ny=@(x)x.^2\r\nz_correct = 0.3334\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n\r\n\r\n%%\r\nx=0:0.01:1;\r\ny=@(x)x.^3\r\nz_correct = 0.25\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T05:49:20.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-10T05:41:31.000Z","updated_at":"2025-11-29T14:58:18.000Z","published_at":"2016-10-10T05:41:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0:0.01:1\\ny=@(x)x.^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(hint: trapz)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47300,"title":"Find Logic 14","description":"Guess the Logic!\r\nlogic(1) = 100\r\nlogic(2) = 96\r\nlogic(3) = 105\r\nlogic(4) = 89\r\nlogic(5) = 114\r\nMake a function logic(x) which will return 'x' th term of sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54px 8px; transform-origin: 54px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 96\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 105\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 89\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43px 8px; transform-origin: 43px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 114\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\n%%\r\nfiletext = fileread('logic.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'elseif') || contains(filetext, 'switch') ; \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 96;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),89))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),114))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),127))","published":true,"deleted":false,"likes_count":7,"comments_count":1,"created_by":293792,"edited_by":223089,"edited_at":"2023-02-22T19:11:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":367,"test_suite_updated_at":"2023-02-22T19:11:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:18:24.000Z","updated_at":"2026-02-14T07:00:09.000Z","published_at":"2020-11-05T07:18:24.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 96\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 105\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 89\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 114\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47315,"title":"Find Logic 16","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 180\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 225\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 120-x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 120;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 225;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":4,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":393,"test_suite_updated_at":"2020-11-07T12:21:32.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-11-05T14:49:56.000Z","updated_at":"2026-02-14T06:59:02.000Z","published_at":"2020-11-05T14:49:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 180\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 225\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47410,"title":"Find Logic 32","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.476px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 155.738px; transform-origin: 174px 155.738px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = 27\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 54\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value equivalent to logic.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 3;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 18;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":206,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T12:03:44.000Z","updated_at":"2026-02-19T09:54:35.000Z","published_at":"2020-11-07T12:03:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = 27\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 54\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value equivalent to logic.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47365,"title":"Find Logic 24","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 341.429px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 170.714px; transform-origin: 174px 170.714px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 27\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(a,b) which will return value equivalent to logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = a-b;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 3;\r\nassert(isequal(logic(b,a),1))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\nassert(isequal(logic(a,b),27))\r\n\r\n%%\r\na = 5;\r\nb = 4;\r\nassert(isequal(logic(b,a),125))","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":211,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T12:07:22.000Z","updated_at":"2026-03-17T20:28:18.000Z","published_at":"2020-11-06T12:07:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 27\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(a,b) which will return value equivalent to logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53940,"title":"Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime","description":"Given three postive integers, ,  and , create the function , defined as follows:\r\n            \r\nWhere  is the th prime and the symbol  is the  fractional part function of a positive real number, defined as follows: \r\n        If  then , where , is the 'floor' of .\r\nFor example for ,  and , we have:\r\n        \r\nTherefore, since :\r\n        \r\nPlease round-off the output to four decimal places, so in this case: .\r\nHINT: This is related to the Faulhaber's formula.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 355px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 177.5px; transform-origin: 407px 177.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven three postive integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 85px; height: 18.5px;\" width=\"85\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 181px; height: 45px;\" width=\"181\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.5px 8px; transform-origin: 77.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime and the symbol \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18.5px;\" width=\"18\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://brilliant.org/wiki/factional-part-function/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efractional part function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a positive real number, defined as follows: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 46px; height: 19px;\" width=\"46\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 86.5px; height: 18.5px;\" width=\"86.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 23px; height: 18.5px;\" width=\"23\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the 'floor' of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36px; height: 18px;\" width=\"36\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAoCAYAAAAFZi8EAAAELUlEQVRoQ+1aS8tNURj+vh8gxEgGXy4DpUguEwwMECVFuYyUcp1JrkkGFCkj11ImbmVKpAyQkkvJFH0/wDU/gOf5rFevtdft7H3ss/Zp7Xo65zvr/j7rfd9nrf2NjpQnCwuMZjGLMomRQkQmm6AQUYjIxAKZTKN4RCEiEwukTWMaqk0GPqVVn6g1C5gB/ATexdoVjwhbiATsBI4AR4GrMYOi/BCwC5it6n6LtS9E+C1Lg5KAqabKngQiLqHOXuAyMA6MAVtVH4fx/ZxryEJE1SoMKfSC98BKY1jWihFB4lYBNLYORfSqh8BigJ4xF/hiD1uI8HsES5YDzxI8Qoy91mVk4xW3TT8LLaImfi5E9IeIBehmEvDc050QSo+gZ1SSfiGiP0SEe/mTJ+gRd413VOqHiKC7zQNmApRuohjW4ft809OLwC6ITa4L5amhKbYW5og5wCZXWPKFJiarzYCWYFQBt4AbAN2LSkLkGctOAJUEFJtdpJxGaPokafjAIP0ggkpqtYH3HBLyCD0JuhRjGzuUzj4oMlb8B8/41ZQFtPeGgsS+mxDByHHK2I3DfQR2+OwUImI3Gl0xE36NT1sRUK6dNeVefZy4YFc1unPT5wk6cOr2xI7rEMGIchDg51JAziEy5Hp8eWCPHyLiDipvMQ1ckksTcQb1jicurkvV6hBhr499XAAYUfjQM5YB/4TyEBESGh6hEb3BfjQR21BI4obt6QcRYpNXioxKKPcRkTIBho41AY9hEfvZburwtPkY6OXibNDEptghdY7MGfdN5cop3UfEaTQ4ZhpRHdnGo7T9bMqZP5ZYs2H5TYAxcp8hoFdVNSyqSZtGokwyEeJGvrCkE7mdfOS4TwI3AL7TZmwndV01udYna6rkXJdH6N3uUkMsfwnQ0C55KEm+qZLqqmrybTCqKCZqVwRx3jXpWOY6H8hVryv7S0x1KoOYC2RY3s8cIeImWb6KoWmX6YCO7XJn4jO0JonMi/xliGOu6FKi5vpTiZDN63sBJHbzynxXaNInZknUDEcHACbwUMiR3MJrj/PG8Dqf2MRm6AR/p8Q1X1SbiWF4v7UxpbIYWv7mRr1m/lhkwvhJfFYOctLAJkLiGMu5i98AP4Ax4ClA+RlSP75kJJ7SNG+0RZy85LHH+44f3gLXHXYgGRuBKaYRvX/c2LHnd9Z699a5PxIi7J0vrutTYW0ZONtxbI/Q1xp13lVIWLOJkFjrVAzZWqfFidnG/oqxeUlVd+dKCLK9SYhoehvaomnaHUoToRVC3VguIchuLyEv9gK+3dVnNJoQIVcScndUlwguTe6gdHiimuLje7mekUkGMxUSIW/kXDO4hx971f7yT1n81xKqLoY6qoc6fQ3GKgMYtU5CHsA0h3/IQkQmHBciChGZWCCTaRSPKERkYoFMplE8IhMifgP+q/MpP3bWugAAAABJRU5ErkJggg==\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; 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\" style=\"width: 430.5px; height: 35px;\" width=\"430.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.5px 8px; transform-origin: 210.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease round-off the output to four decimal places, so in this case: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152px; height: 18.5px;\" width=\"152\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This is related to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFaulhaber's formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FPSP(x,e,n)\r\n    y = FPSP(x,e,n);\r\nend","test_suite":"%%\r\nx = 10; e = 2; n = 6;\r\ny_correct = 0.6154;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 3; n = 50;\r\ny_correct = 0.6288;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 4; n = 100;\r\ny_correct = 0.2495;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 250; e = 5; n = 200;\r\ny_correct = 0.1415;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 123; e = 6; n = 200;\r\ny_correct = 0.1292;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 10; e = 10; n = 300;\r\ny_correct = 0.7006;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 1234; e = 56; n = 789;\r\ny_correct = 0.8419;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 3000; e = 300; n = 3000;\r\ny_correct = 0.6441;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nxs = 20:2:2000;\r\nys = arrayfun(@(x) FPSP(x,x/2,x),xs);\r\nss = round([sum(ys) nnz(ys) mean(ys) mode(ys) median(ys) std(ys)],4); \r\nss_correct = [472.0982 numel(xs) 0.4764 0.2518 0.4704 0.2854];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('FPSP.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2022-01-20T12:19:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-19T18:18:26.000Z","updated_at":"2026-03-28T13:08:19.000Z","published_at":"2022-01-20T10:08:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven three postive integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,y,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,e,n)=\\\\left\\\\{ \\\\frac{1}{p_{n}} \\\\cdot \\\\sum^{x}_{i=1} i^{e}\\\\right\\\\}  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime and the symbol \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://brilliant.org/wiki/factional-part-function/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efractional part function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a positive real number, defined as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er \\\\in \\\\mathbb{R}^{+}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}=r-\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the 'floor' of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sum^{10}_{i=1} i^{2} = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_6=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=\\\\left\\\\{ \\\\frac{385}{13} \\\\right\\\\}  = \\\\{29.615384561538...\\\\}=0.61538461538...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off the output to four decimal places, so in this case: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=0.6154\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is related to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFaulhaber's formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43278,"title":"Make roundn function","description":"Make roundn function using round.\r\n\r\n  x=0.55555\r\n  y=function(x,1)\r\n  y=1\r\n\r\n  y=function(x,2)\r\n  y=0.6\r\n\r\n  y=function(x,3)\r\n  y=0.56\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eMake roundn function using round.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex=0.55555\r\ny=function(x,1)\r\ny=1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey=function(x,2)\r\ny=0.6\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey=function(x,3)\r\ny=0.56\r\n\u003c/pre\u003e","function_template":"function y = myroundn(x,n)\r\n  y = \r\nend","test_suite":"%%\r\nx = 0.5555;\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.5555;\r\nn = 2;\r\ny_correct = 0.6;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.5555;\r\nn = 3;\r\ny_correct = 0.56;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 1;\r\ny_correct = 0;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 2;\r\ny_correct = 0.1;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 3;\r\ny_correct = 0.11;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 1;\r\ny_correct = 4;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 2;\r\ny_correct = 4.3;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 3;\r\ny_correct = 4.27;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 4;\r\ny_correct = 4.274;\r\nassert(isequal(myroundn(x,n),y_correct))","published":true,"deleted":false,"likes_count":30,"comments_count":3,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4518,"test_suite_updated_at":"2016-11-22T18:46:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-09T12:34:11.000Z","updated_at":"2026-04-02T02:10:47.000Z","published_at":"2016-10-09T12:34:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake roundn function using round.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0.55555\\ny=function(x,1)\\ny=1\\n\\ny=function(x,2)\\ny=0.6\\n\\ny=function(x,3)\\ny=0.56]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47400,"title":"Find Logic 30","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 371.381px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 185.69px; transform-origin: 174px 185.69px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 44\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 49\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 51\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 56\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(9) = 56\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(10) = 57\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 42;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 44;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 50;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 51;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 55;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":195,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T11:28:49.000Z","updated_at":"2026-02-19T09:55:45.000Z","published_at":"2020-11-07T11:28:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 44\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 49\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 51\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 56\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(9) = 56\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(10) = 57\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47405,"title":"Find Logic 31","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.476px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 155.738px; transform-origin: 174px 155.738px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 23\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 19\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 31\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 41\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = -1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 21;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 23;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 19;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 31;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 41;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = -1;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":195,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T11:49:35.000Z","updated_at":"2026-02-14T13:50:16.000Z","published_at":"2020-11-07T11:49:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 19\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 31\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = -1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44449,"title":"Moving Median Absolute Deviation","description":"The median absolute deviation (MAD) is defined as\r\nMAD = median(abs(A − median(A)))\r\nfor a rolling window of length n. For example:\r\nmove_mad(1:10, 5) \r\nreturns [1 1 1 1 1 1];\r\n\r\nmove_mad(logspace(0, 1, 10), 3) \r\nreturns [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]\r\nRound the result to 3 digits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.8px; transform-origin: 407px 112.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe median absolute deviation (MAD) is defined as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 128px 8.5px; transform-origin: 128px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 76px 8.5px; transform-origin: 76px 8.5px; \"\u003eMAD = median(abs(A \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(255, 0, 0); border-block-start-color: rgb(255, 0, 0); border-bottom-color: rgb(255, 0, 0); border-inline-end-color: rgb(255, 0, 0); border-inline-start-color: rgb(255, 0, 0); border-left-color: rgb(255, 0, 0); border-right-color: rgb(255, 0, 0); border-top-color: rgb(255, 0, 0); caret-color: rgb(255, 0, 0); color: rgb(255, 0, 0); column-rule-color: rgb(255, 0, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(255, 0, 0); perspective-origin: 8px 8.5px; text-decoration: none; text-decoration-color: rgb(255, 0, 0); text-emphasis-color: rgb(255, 0, 0); transform-origin: 8px 8.5px; \"\u003e− \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; \"\u003emedian(A)))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a rolling window of length n. For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emove_mad(1:10, 5) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003ereturns \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 52px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 52px 8.5px; \"\u003e[1 1 1 1 1 1]\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 128px 8.5px; transform-origin: 128px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emove_mad(logspace(0, 1, 10), 3) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 228px 8.5px; transform-origin: 228px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003ereturns \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 196px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 196px 8.5px; \"\u003e[0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRound the result to 3 digits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function stats = move_mad(v, n)\r\n    \r\nend","test_suite":"%%\r\nv = 1:10;\r\nn = 5;\r\nstats_correct = [1 1 1 1 1 1];\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);\r\n\r\n%%\r\nv = logspace(0, 1, 10);\r\nn = 3;\r\nstats_correct = [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748];\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);\r\n\r\n%%\r\nrng('default');\r\nv = randn(1000, 1);\r\nn = 990;\r\nstats_correct = 0.660 * ones(1, 11);\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);","published":true,"deleted":false,"likes_count":0,"comments_count":6,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2021-07-03T05:49:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-12T08:08:02.000Z","updated_at":"2025-11-18T17:43:42.000Z","published_at":"2017-12-12T08:08:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe median absolute deviation (MAD) is defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[MAD = median(abs(A − median(A)))]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor a rolling window of length n. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[move_mad(1:10, 5) \\nreturns [1 1 1 1 1 1];\\n\\nmove_mad(logspace(0, 1, 10), 3) \\nreturns [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRound the result to 3 digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57646,"title":"Easy Sequences 93: Recursive Polynomial Function","description":"For a natural number  and a polynomial function , we define a recursive function , as follows:\r\n                ,  and\r\n                ,  for .\r\nFor example, if  (or in Matlab array form, P = [1 2 1]):\r\n                \r\n                \r\n                \r\n                \r\n                ...\r\n                \r\n                and so on...\r\nWe can see that  can grow very quickly. Therefore, we will instead calculate: , that is, is equal to the logarithm (base-) of the absolute value of .\r\nGiven a polynomial array , and an integer , find the value of , rounded-off to 4 decimal places.\r\n----------------------\r\nNOTE: To encourage vectorization , FOR and WHILE loops are disabled. If you know the math, this problem can be solved in less than 15 lines of code. However, solutions up to 50 lines of code will still be accepted. The semicolon (;), shall be considered as an end-of-line character. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 505px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 252.5px; transform-origin: 407px 252.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31.5px; height: 18.5px;\" width=\"31.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define a recursive function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 18.5px;\" width=\"79\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 167.5px; height: 18.5px;\" width=\"167.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 118.5px; height: 19.5px;\" width=\"118.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or in Matlab array form, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44px 8px; transform-origin: 44px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; \"\u003eP = [1 2 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 318.5px; height: 19.5px;\" width=\"318.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan 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\" style=\"width: 326px; height: 19.5px;\" width=\"326\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 118px; height: 18.5px;\" width=\"118\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                and so on...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe can see that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can grow very quickly. Therefore, we will instead calculate:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 108.5px; height: 18.5px;\" width=\"108.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis equal to the logarithm (base-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the absolute value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a polynomial array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, rounded-off to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55px 8px; transform-origin: 55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e----------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization , \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFOR and WHILE loops are disabled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If you know the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003emath\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, this problem can be solved in less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e15\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lines of code. However, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esolutions up to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003e50\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e lines of code will still be accepted\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52px 8px; transform-origin: 52px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The semicolon (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159px 8px; transform-origin: 159px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), shall be considered as an end-of-line character. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = T(P,x)\r\n    t = round(log(abs(R(x))),4);\r\n    function r = R(x)\r\n        if x == 0\r\n            r = polyval(P,x);\r\n        else\r\n            r = x * R(x-1) + polyval(P,x);\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nP = [1 2 1]; x = 0:10;\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [0.0000 1.6094 2.9444 4.2905 5.7589 7.3908 9.1876 11.1344 13.2140 15.4113 17.7139];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [1 0 1]; x = [10 100 1000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [17.2030 365.8380 5914.2268];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [-1 1 -1 1]; x = [10 100 1000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [17.2030 365.8380 5914.2268];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [1 2 3 4 5]; x = [10 100 1000 10000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [19.7933 368.4283 5916.8171 82113.6167];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [11 -22 33 -44 55 -66]; x = 12345;\r\nt = T(P,x);\r\nt_correct = 103969.6836;\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = 2:2:10; x = P.*200;\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [2005.8827 4557.3328 7317.9383 10214.4041 13211.9064];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = 2:2:100; x = P./2;\r\nt = arrayfun(@(i) T(P,i),x);\r\ns = round([mean(t) median(t) mode(t) std(t)],4);\r\ns_correct = [163.8877 167.4357 7.8823 59.1051];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('T.m');\r\nnot_allowed = contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'java') || contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)\r\nassert(count(filetext, 'function')==1)\r\n\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=50)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-14T06:56:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2023-02-07T04:59:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-03T04:56:19.000Z","updated_at":"2025-11-26T02:41:15.000Z","published_at":"2023-02-06T08:01:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we define a recursive function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(0)=P(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x) = x\\\\cdot R(x-1) + P(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x) = x^2+2x+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or in Matlab array form, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP = [1 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(0) = P(0)=0^2+2\\\\cdot 0 + 1=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(1) = 1\\\\cdot R(0)+P(1)=1\\\\cdot 1+1^2+2\\\\cdot 1 + 1=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(2) = 2\\\\cdot R(1)+P(2)=2\\\\cdot 5+2^2+2\\\\cdot 2 + 1=19\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(3) = 3\\\\cdot R(2)+P(3)=3\\\\cdot 19+3^2+2\\\\cdot 3 + 1=73\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(10) = 49320491\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                and so on...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can see that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can grow very quickly. Therefore, we will instead calculate:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x) = \\\\text{log}|R(x)|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis equal to the logarithm (base-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the absolute value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a polynomial array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, rounded-off to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e----------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization , \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFOR and WHILE loops are disabled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If you know the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emath\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, this problem can be solved in less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e15\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lines of code. However, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esolutions up to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e50\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e lines of code will still be accepted\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The semicolon (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), shall be considered as an end-of-line character. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47390,"title":"Find Logic 29","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 371.381px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 185.69px; transform-origin: 174px 185.69px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 40\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,4) = 85\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 32\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 65\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,3) = 108\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,2) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,3) = 175\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5,1) = 156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(a,b) which will return value according to problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = 4;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 1;\r\ny_correct = 4;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ny_correct = 15;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ny_correct = 65;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 4;\r\nb = 2;\r\ny_correct = 120;\r\nassert(isequal(logic(a,b),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T02:37:38.000Z","updated_at":"2026-02-25T13:59:58.000Z","published_at":"2020-11-07T02:37:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 40\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,4) = 85\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 65\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,3) = 108\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,2) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,3) = 175\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5,1) = 156\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(a,b) which will return value according to problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53725,"title":"Easy Sequences 56: Counting \"Ugly\" Numbers","description":"A positive integer  is called a regular number, if and only if there exist a non-negative integer , such that .  For some reason, such a number is also refered to as an ugly number. Below are the first few regular numbers:\r\n                            \r\nIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only  regular numbers  and just  regular numbers .\r\nGiven an integer , and exponent , we are tasked to write a function that counts the number of regular numbers less than or equal to .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 174px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA positive integer\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Regular_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is called a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Regular_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eregular number, \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eif and only if there exist a non-negative integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"20\" style=\"width: 49px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.  For some reason, such a number is also refered to as an \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eugly number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Below are the first few regular numbers:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"515.5\" height=\"19\" style=\"width: 515.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e regular numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"19\" style=\"width: 42.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and just \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF4AAAAkCAYAAAAAa43JAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXqADAAQAAAABAAAAJAAAAAB8lvLWAAAGp0lEQVRoBe2Ye4hVVRSHx0dak4qZSlk2FqZRmeYDrNCyUsmCSuuPqLSyMiqKDMpK7EmGKVIWZC+SSv9IRQhNBaWH9LJU1MxHzoi9yLR8VZaP+n7jXrHYnHPvmbl3tMf5wTd7n7XXXmfvdfbe59ypqMiVZyDPQJ6BPAN5BvIM5Bn4L2SgUT0mMZI+/WAirC7Qv5K2y6ALVME2WAMz4VdoaLXmBgOhD2gMnWEA/AheykFP6AtnQQ18CEvhN6ir2tJhAlTDE3XtnOavSeyFP2FQmhP2UfAD7IMF8DroIamf7EpIQ6kXgeeBxnkAPoYx0BVitcMwHzSuFTALND5dfwOab101hw7qr4dXFh1NlPWgoCIt8SNC+0+UZ4JJK+tRUN9d0APKqWYEewmUbN1jE/SHNHWgQcmV7yTQ+CSVM0B2rfhhkFW34Kh+omyJf9EFVeCkxDfBvjP43U8ZqzGGL0D9p8aNJVzrWFkMNmntsFZF4slH/hpvy8i3Oddfgtq3QAsoplNx2A02hrIk/vIQcK0LnJR4rWK78dXUkzQdo3x03pdLcwlk932buq3etPg6021n6AEkaRxGizk2ycHZmlL/BGpgD6hfwcRrBRbTcTi8DAthShHnE1x7d1f31ePDhSZeDl1LkCEh0NeUI0ATL6QLaLSHsyHFUWe16R6rpJQPY+8Nw0E7qCzSi0pfJDoTbwdNSiSteCXb2ndQ9w+Cy4pK+B3kMw1KVTsCbAW75yUZA77i+oxM6XOE81F8zT9J52HUR8T40KijSf4FV3zwTS3uDEGuCh7FEi83+3rRzddDRxmDJlLKrhevzsRS9SYBFE98D9rBR0LXgM7qJL2H0fqNTnIINi0e8zs/wU/vhmpYBnpQUsmJP50g+t72KzNL4s+hj51zGrSSfCvYKvuK+hlQqjTpP8ASs4T6ItARZjYlTuPvBF6zuTCfyb4hqm90fjdHbbpUbH35KFemkhLfjCjLYRO0AlOWxMtXn2B2pNgEVb4AWpHl0JUE8bFV15j1PpoP28HatRt0DJomUbE27cpG1hCVK5zf3VGbPh4U467IXlLiJxBsP/SLgmZNvLoNAJuclfpxcrEay6BxxLC4SQnQR8Fnzudzd0/Ny/cd4tqsWklll/PTgzadSEU7eSHED20LNsWu8xmvhCnpT0GsrInXoKeBBqDjyk9SsXX0lKrnCWBx9es0SVUYdT/zG+yc3nd27Y7+oU2J7AbvgPVT2R4ktS+CbdABYtUr8a2Jshm0ZXXcxMqSeB1Netoa7GtwFIwHnwDVh0IpeoPOlpjnCgTSV5n5PeL82lJf5drk8x38HGxKrPVbR910LxXZddQkKVPim0Y9n+G6I0wGrfxYZztDL+p6+tJK0DkqTQK9YPXLbxTorH8AtEpmgCasr48pMBfUXh/Z/dRXL9k06bixz8xTnNNW6n1gOFwDJ8EOWAvaDVUwBqQlB4uK0yifhHWg7/XBEKtlMGgRW7t2/Qexo7/2LxN72lnK60OQnpQHQH0eCzZfqH03WEx/bnq/LPU7XByt/jT5XTonzSmyN+FaP8ZsnEND+xXOZm1Zyo2h/9+FVp6XklYI3cTLfM3em0bbBZ96x1BfRjnT2Uv5lveT0Ys0TTYetVenOUX2UVzrBSrNgtm1tYMPwuacVgbX2sJ89ntjfep+9QxKCHAfNlsB5ya0y6Sz0Xx0XtZX+iy181i7qDIl0EPY7X63pfh4s47QPaHPt5RtfGOG+pbQV++5VMUrPtUxY8NHzk/nYZI2O6POU6+TubgRuntjSl3JmR7a9C/rS1P8tAslvQcW1NbS/xxL01vQHPSwRoA+Gw+7iq34ZoxwJ2jQK0FnZazHMah9O2iiJq00bU217QNNupi64qA46rMcWoCXjiAlXO3P+oaE+oXY7FzXy/C6BJ8spkwrPksg71Ms8fK9CPQzWpPV+dgWTDdQ0VeM2oaB11guZDfW+MYC9b607Qr95lFq10jtYSko3rtwDCRJ/8jTl5g9dD3AHkmOGW0NkvibuLklpn+BgWj1rAi+erHoRagtq76a2ECI5RMoP/VrHDulXGssG8DGprNZ/X+BpyH+bMZUMRp0Divhe2Ex6LPSv4y5rLM200PjULxUlXqT1MChoRulvlzagbbxeqgGTTZJrTF2gFehDXSBrNJcdJ53Bv1o0xfUatCxlaSpGGtgFejd9I84yxnHYVMVd9Zx9OBhG8H/8MbaIdoZC0GrNtchyoDOZr3omhyi++W3CRnolGciz0CegTwDeQbyDPzbM/AX1/saI8Kkgp8AAAAASUVORK5CYII=\" width=\"47\" height=\"18\" style=\"width: 47px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e regular numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"19\" style=\"width: 40px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, we are tasked to write a function that counts the number of regular numbers less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = regCount(n,e)\r\n    c = n ^ e;\r\nend","test_suite":"%%\r\nn = 10; e = 5;\r\nc_correct = 313;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 10; e = 10;\r\nc_correct = 2053;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 2; e = 100;\r\nc_correct = 48694;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 7; e = 77;\r\nc_correct = 473183;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 10; e = 100;\r\nc_correct = 1697191;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 77; e = 77;\r\nc_correct = 5166439;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\n%ns = 1:100; es = ns+10;\r\n%cs = arrayfun(@(i) regCount(ns(i),es(i)),1:100);\r\n%ss = floor([cs(25:25:end) sum(cs) std(cs) sum(num2str(cs))]);\r\n%ss_correct = [203379 1797050 6815143 17856016 421336320 5052973 44715];\r\n%assert(isequal(ss,ss_correct))\r\n%%\r\nns = 1:25; e = 100;\r\ncs = arrayfun(@(i) regCount(ns(i),e),1:25);\r\nss = floor([cs(5:10:end) sum(cs) std(cs) sum(num2str(cs))])\r\nss_correct = [585064 2751849 4607635 57125382 1487797 10278];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('regCount.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":27,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2021-12-19T18:30:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-17T16:20:39.000Z","updated_at":"2026-03-19T15:29:37.000Z","published_at":"2021-12-17T17:33:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Regular_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is called a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Regular_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eregular number, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003eif and only if there exist a non-negative integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\\\\ |\\\\ 60^k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.  For some reason, such a number is also refered to as an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eugly number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Below are the first few regular numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60...\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2,053\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e regular numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le10^{10}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and just \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e48,694\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e regular numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le2^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are tasked to write a function that counts the number of regular numbers less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53755,"title":"Easy Sequence 61: Wide Pythagorean Triangles","description":"An integer-sided right triangle with sides , is called a \"wide Pythagorean triangle\", if , and . \r\nWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit .\r\nBelow is the list of all Pythagorean triangles with all sides :\r\n    \r\nTherefore, for , your program output should be . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111.25px; transform-origin: 407px 111.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128px 8px; transform-origin: 128px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn integer-sided right triangle with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 47.5px; height: 18.5px;\" width=\"47.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is called a \"wide Pythagorean triangle\", if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 61px; height: 18px;\" width=\"61\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 60px; height: 18px;\" width=\"60\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 102.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 51.25px; text-align: left; transform-origin: 384px 51.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-45px\"\u003e\u003cimg 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\" style=\"width: 745px; height: 102.5px;\" width=\"745\" height=\"102.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 50px; height: 18px;\" width=\"50\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, your program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = countWPTs(s)\r\n    c = length(primes(s)) + 20;\r\nend","test_suite":"%%\r\ns = 100;\r\nc_correct = 45;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 300;\r\nc_correct = 196;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000;\r\nc_correct = 857;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000;\r\nc_correct = 12397;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000;\r\nc_correct = 161208;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000000;\r\nc_correct = 1979930;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000000;\r\nc_correct = 23469232;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000000;\r\nc_correct = 271353574;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\nss = floor((pi/2) .^ (11:40));\r\ncs = arrayfun(@(s) countWPTs(s),ss);\r\nss = [sum(cs) nnz(find(cs)) floor(std(ss)) sum(num2str(cs))];\r\nss_correct = [487155754 30 15528091 13675];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('countWPTs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-05T05:25:43.000Z","updated_at":"2025-11-21T18:31:53.000Z","published_at":"2022-01-05T08:26:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn integer-sided right triangle with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[a,b,c]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is called a \\\"wide Pythagorean triangle\\\", if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb \\\\ge a+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec \\\\ge b+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\ [6,8,10],\\\\ [9,12,15],\\\\ [8,15,17],\\\\ [12,16,20],\\\\ [15,20,25],\\\\ [10,24,26],\\\\ [18,24,30],\\\\ [16,30,34],\\\\ [21,28,35],\\\\ \\\\\\\\\\n\\\\ \\\\ [12,35,37],\\\\ [15,36,39],\\\\ [24,32,40],\\\\ [27,36,45],\\\\ [30,40,50],\\\\ [14,48,50],\\\\ [24,45,51],\\\\ [20,48,52],\\\\ [28,45,53],\\\\ \\\\\\\\\\n\\\\ \\\\ [33,44,55],\\\\ [40,42,58],\\\\ [36,48,60],\\\\ [39,52,65],\\\\ [25,60,65],\\\\ [16,63,65],\\\\ [33,56,65],\\\\ [32,60,68],\\\\ [42,56,70],\\\\ \\\\\\\\\\n\\\\ \\\\ [48,55,73],\\\\ [24,70,74],\\\\ [45,60,75],\\\\ [21,72,75],\\\\ [30,72,78],\\\\ [48,64,80],\\\\ [18,80,82],\\\\ [51,68,85],\\\\ [40,75,85],\\\\ \\\\\\\\\\n\\\\ \\\\ [36,77,85],\\\\ [60,63,87],\\\\ [39,80,89],\\\\ [54,72,90],\\\\ [35,84,91],\\\\ [57,76,95],\\\\ [62,72,97],\\\\ [60,80,100],\\\\ [28,96,100]\\\\ \\\\}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, your program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e45\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53109,"title":"Easy Sequences 52: Non-squarable Rectangles ","description":"Any integer-sided rectangle can be cut into unit rectangles () and rearranged into sets of smaller rectangles. For example the  rectangle can be broken as follows:\r\n                                                      \r\nWe call an integer rectangle as \"squarable\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of non-unit squares of equal sizes. For example the  rectangle can be broken into six  squares. Therefore, the  rectangle is squarable.\r\n                                                \r\nInteger rectangles that are not squarable are called \"non-squarable\". The  rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area  square units are as follows:\r\n\r\nCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit . \r\nFor , the program should output:\r\n        \r\nNOTE: Reflections and rotations are not significant and should be counted only once.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 544px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 272px; transform-origin: 407px 272px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.5px 8px; transform-origin: 188.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAny integer-sided rectangle can be cut into unit rectangles (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAkCAYAAADfJffWAAABK0lEQVRoge2YUQ2DMBBAnwcc1AA+UFAHc1AHWEDDJMzDLEzDLGwfhaxkhNBysN5yL2n4uvZ4NL0rYBiGYRi144Dm10nsoJWczAED8JKe+CQ88ACuEpM1fGRMQ5OUjihjyn23lA4I4/OOPik9cBmHmJSUgD4pKdVKaYEncefl4Mc4V7guVCwlPZu2ivFJTF+4LlQsBfLESAmByqXANjGSQkCBFFgXIy0ElEiBZTFHCAFFUmAupucYIaBMCnx3zNJCQKGUtOPMKdc5qJKSniHpHUVajBopS4dqSYO3BRVS1qrMEWKql7Kl7EqLqVpKTh8iKUZcimN+CIbCeUoaMwkx6Qd9sO+2jSMmf1sYA7GU5jC9YG4fUhrniTtjKf9ARf+F/MlxhmEYhmEYf8Ub9AbIMJOfOosAAAAASUVORK5CYII=\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167px 8px; transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and rearranged into sets of smaller rectangles. For example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.5px 8px; transform-origin: 113.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle can be broken as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 80.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 40.25px; text-align: left; transform-origin: 384px 40.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                      \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 246px;height: 75px\" 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bj45ODQ8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KO1Qc/QAAABxpRE9UAAAAAgAAAAAAAACWAAAAKAAAAJYAAACWAAAVm4ZFF1QAABVnSURBVHgB7N1BdiXF0QZQyUtohniGd4A99toZAzswMxjCEpCxdSIHnH7odFGNIuK7nlT90E+uuJGZld/Llv/nl9/+8+Q/BAgQIECAAAECBAgQIECAwJ8SeBaw/5SfDxMgQIAAAQIECBAgQIAAgf8LCNgGAgECBAgQIECAAAECBAgQuEFAwL4B0Y8gQIAAAQIECBAgQIAAAQICtjFAgAABAgQIECBAgAABAgRuEBCwb0D0IwgQIECAAAECBAgQIECAgIBtDBAgQIAAAQIECBAgQIAAgRsEBOwbEP0IAgQIECBAgAABAgQIECAgYBsDBAgQIECAAAECBAgQIEDgBgEB+wZEP4IAAQIECBAgQIAAAQIECAjYxgABAgQIECBAgAABAgQIELhBQMC+AdGPIECAAAECBAgQIECAAAECArYxQIAAAQIECBAgQIAAAQIEbhAQsG9A9CMIECBAgAABAgQIECBAgICAbQwQIECAAAECBAgQIECAAIEbBATsGxD9CAIECBAgQIAAAQIECBAgIGAbAwQIECBAgAABAgQIECBA4AYBAfsGRD+CAAECBAgQIECAAAECBAgI2MYAAQIECBAgQIAAAQIECBC4QUDAvgHRjyBAgAABAgQIECBAgAABAgK2MUCAAAECBAgQIECAAAECBG4QELBvQPQjCBAgQIAAAQIECBAgQICAgG0MECBAgAABAgQIECBAgACBGwQE7BsQ/QgCBAgQIECAAAECBAgQICBgGwMECBAgQIAAAQIECBAgQOAGAQH7BkQ/ggABAgQIECBAgAABAgQICNjGAAECBAgQIECAAAECBAgQuEFAwL4B0Y8gQIAAAQIECBAgQIAAAQICtjFAgAABAgQIECBAgAABAgRuEBCwb0D0IwgQIECAAAECBAgQIECAgIBtDBAgQIAAAQIECBAgQIAAgRsEBOwbEP0IAgQIECBAgAABAgQIECAgYBsDBAgQIECAAAECBAgQIEDgBgEB+wZEP4IAAQIECBAgQIAAAQIECAjYxgABAgQIECBAgAABAgQIELhBQMC+AdGPIECAAAECBAgQIECAAAECArYxQIAAAQIECDz98s9/UAgU+PDdf1ZWbTy/tnVrf1cOWkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KaAQPIm0co/sDWAGc+vw3Vrf1dORkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KaAQPIm0co/sDWAGc+vw3Vrf1dORkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KbAo0Dy4dtv3vzs5D/w/Le/P728vDw9vfw0uYw3n/2Xf/37o39mawBLG89p/f3oYPYPCTQRELCbNMJjECBAgACB9xRICyTH+vnLp+fn56eXX388/2jjTVoASxvPaf3dOEfVtEdAwN7TS5UQIECAAIHLAmmBpKCcYGf9/8He+jcyBOya0a4E3l9AwH7/HngCAgQIECDw7gKpAfvJCfa7j73P8QBp41nA/hyjyM8kcE1AwL7m5lMECBAgQGCVQFogqeY5wXaCXWNh8lXAntw9z75NQMDe1lH1ECBAgACBCwKpAdsJtoB9Ybq0+4iA3a4lHihYQMAObr7SCRAgQIBACaQGbCfYAnbNgclXAXty9zz7NgEBe1tH1UOAAAECBC4IpAZsJ9gC9oXp0u4jAna7lnigYAEBO7j5SidAgAABAiWQGrCdYAvYNQcmXwXsyd3z7NsEBOxtHVUPAQIECBC4IJAasJ1gC9gXpku7jwjY7VrigYIFBOzg5iudAAECBAiUQGrAdoItYNccmHwVsCd3z7NvExCwt3VUPQQIECBA4IJAasB2gi1gX5gu7T4iYLdriQcKFhCwg5uvdAIECBAgUAKpAdsJtoBdc2DyVcCe3D3Pvk1AwN7WUfUQIECAAIELAqkB2wm2gH1hurT7iIDdriUeKFhAwA5uvtIJECBAgEAJpAZsJ9gCds2ByVcBe3L3PPs2AQF7W0fVQ4AAAQIELgikBmwn2AL2henS7iMCdruWeKBgAQE7uPlKJ0CAAAECJZAasJ1gC9g1ByZfBezJ3fPs2wQE7G0dVQ8BAgQIELggkBqwnWAL2BemS7uPCNjtWuKBggUE7ODmK50AAQIECJRAasB2gi1g1xyYfBWwJ3fPs28TELC3dVQ9BAgQIEDggkBqwHaCLWBfmC7tPiJgt2uJBwoWELCDm690AgQIECBQAqkB2wm2gF1zYPJVwJ7cPc++TUDA3tZR9RAgQIAAgQsCqQHbCbaAfWG6tPuIgN2uJR4oWEDADm6+0gkQIECAQAmkBmwn2AJ2zYHJVwF7cvc8+zYBAXtbR9VDgAABAgQuCKQGbCfYAvaF6dLuIwJ2u5Z4oGABATu4+UonQIAAAQIlkBqwnWAL2DUHJl8F7Mnd8+zbBATsbR1VDwECBAgQuCCQGrCdYAvYF6ZLu48I2O1a4oGCBQTs4OYrnQABAgQIlEBqwHaCLWDXHJh8FbAnd8+zbxMQsLd1VD0ECBAgQOCCQGrAdoItYF+YLu0+ImC3a4kHChYQsIObr3QCBAgQIFACqQHbCbaAXXNg8lXAntw9z75NQMDe1lH1ECBAgACBCwKpAdsJtoB9Ybq0+4iA3a4lHihYQMAObr7SCRAgQIBACaQGbCfYAnbNgclXAXty9zz7NgEBe1tH1UOAAAECBC4IpAZsJ9gC9oXp0u4jAna7lnigYAEBO7j5SidAgAABAiWQGrCdYAvYNQcmXwXsyd3z7NsEBOxtHVUPAQIECBC4IJAasJ1gC9gXpku7jwjY7VrigYIFBOzg5iudAAECBAiUQGrAdoItYNccmHwVsCd3z7NvExCwt3VUPQQIECBA4IJAasB2gi1gX5gu7T4iYLdriQcKFhCwg5uvdAIECBAgUAKpAdsJtoBdc2DyVcCe3D3Pvk1AwN7WUfUQIECAAIELAqkB2wm2gH1hurT7iIDdriUeKFhAwA5uvtIJECBAgEAJpAZsJ9gCds2ByVcBe3L3PPs2AQF7W0fVQ4AAAQIELgikBmwn2AL2henS7iMCdruWeKBgAQE7uPlKJ0CAAAECJZAasJ1gC9g1ByZfBezJ3fPs2wQE7G0dVQ8BAgQIELggkBqwnWAL2BemS7uPCNjtWuKBggUE7ODmK50AAQIECJRAasB2gi1g1xyYfBWwJ3fPs28TELC3dVQ9BAgQIEDggkBqwHaCLWBfmC7tPiJgt2uJBwoWELCDm690AgQIECBQAqkB2wm2gF1zYPJVwJ7cPc++TUDA3tZR9RAgQIAAgQsCqQHbCbaAfWG6tPuIgN2uJR4oWEDADm6+0gkQIECAQAmkBmwn2AJ2zYHJVwF7cvc8+zYBAXtbR9VDgAABAgQuCKQGbCfYAvaF6dLuIwJ2u5Z4oGCBdgH70Qs+uEdKJ0BgmMCH73ZuWIe1weN+osCj9++Hb7/5xJ806487wd65XqWN57SA/ai/s1YfT/upAlP2VwL2p3bWnydAgMAbAlNeAG+U4V+HCTzasG4P2E6wBewNU13A3tBFNbwlMGV/JWC/1Un/ngABAp8oMOUF8Ill+ePLBR4F7C++/+Hp5eXl6fn52XWww6P+bl2vHtW7dTw/qjetv8uX6fjypoxnATt+qAIgQOBugSkvgLvr9vNmC/zRBl24nv/lws9ff/XRAbp1vUobz/r70eHtHy4TmLJeCdjLBp5yCBB4f4EpL4D3l/IEnQQeBhK/g92pTZefxV8hfqXb+isP+nt5avjgIIEp+ysBe9Cg8qgECMwQmPICmKHpKf8qgdSA7Xew/Q72XzXHPud/j4D9OXX97C4CU/ZXYwL21m8ca8Cm/K+YqvenIlh9TRnPaRua1YNWcU+pAdt6JWBvmP5p7yPr1e795PTxLGB3WVWfv3z9H5D59ccuT/R5n0O9n9f3vX96SH+nvwDee5j47+8lkLphdYItYPeaideeJu19ZL3anRemj2cB+9o6dvunUr5BLzj1lsTOa0p/p78Ado4+VV0VSN2wWq8E7KtzptPn0t5H1isn2J3m3++fRcD+vch7/d8hJ36HV72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVwKMNa/17150CH77LCtg7u/i4qrT+fvj2m8cYC/6N/dWM9UrA7jLZQk78Drd6D8XKm5D+CtgrR29sUQJ2ZuvTAlhal9P6uz1g+xs3AvalNezRC/6L7394enl5eXp+fnblYByYBy3WgUfr1dYNzaVF3YfGCDwaz2MK8KCXBLauV8bz63BI66+8sCMnPZq/U8bznBPs3/4Kk3C9Y9Looz5u+bLs56+/+uiGdsoL4KMP7x/GCjza0MSChBS+db0ynl8HcFp//1evfeb8feb0/dWcgO13Kla96lN+h6Sapt6S2HX1V8R39TO9GoEkcwSkBbC0Lqf1d/tfEU/ZT07fXwnYXVbakN9ZPdzqPRQrb0L6O/0FsHLsKeqygIB9mW70B9MC2OhmXXj4tP5uD9h+B3vG72D/FwAA//8vMK6DAAAX/0lEQVTt3bF2JUmRxvEW3ri9JnjwBoC9T7MHbx4Gj8PTjD3DG4AH5uKOt70jdCKPUOkOXXXrqjLj+7WTqWpV3Yp/RGTGlyF1P3356c+nif7883e/efdtPn//3bvXu1x8+sWvPv3LFV/+0cWkn7WDvT+LZ/m/TPHvP3//3+/66vMPf333uosIIIAAAgggcD8BeqG3Xli9vnoisO9P8lOe8PTLT09PT5++/N/fT3nc9A9h7/QuuusFQ/y7+gZwl4/djAACCCCAwEUEUgX2J/XVRRG372MJ7H28HvbdKR2/AsjeItFzTPEvgd0zflmFAAIIIDA3gVSBrb5a4ycECexZ1o+QE6mBm70DRctJiH8J7JbRyygEEEAAgckJpApsHWwC+1BqpiZMyolUBQV7i0TPMcW/BHbP+GUVAggggMDcBOgFv4M9c4TqYM/inZCO38DN3oGi5STEvwR2y+hlFAIIIIDA5ARSBbYOtg72odRMTZiUjl8FBXuLRM8xxb8Eds/4vdeqH//0x0/f/OHbex/jfgQQQACBGwToBR3sG6ExxWUd7Cnc8NNLhHT8Bm72DhQtJyH+JbBbRu/dRj0Xft/8z7dE9t0kPQABBBB4n0CqwE7RC6vXVwT2+3n74VdTOn4Flr1FoueY4t/VN4Ce0Xe9VVX4EdnX+8IbIIBATwK1zr617vP337291Opr9ZUfET8U0KkJk3IiNYIipMPJ3t7/rzuBPSLc5BWB1/sYkf0KjCkCCCBwEoHX6+zrR3YX2Cl6YfX6Sgf7dVZeOE85kSrE7C0SPccU/66+AfSMvuutelv4EdnX+8QbIIBALwJv19myrrvAVl/pYFes7xpTEyblRGoEgw72QNFyEuJfArtl9N5t1Hv7GJF9N1YPQAABBAaB99bZ57/sLrBT9MLq9ZUO9kjVaycpJ1JFmb1FoueY4t/VN4Ce0Xe9VbcKPyL7et94AwQQ6EHg1jrbXWCrr3SwD2VwasKknEiNoAjpcLLX72CPGDCJIXBrH3sGQGTHhAFDEUDggQRurbPdBXaKXli9gaGD/cDk3/PolBOpYsLeItFzTPHv2RvA8/+f7M/6BH7888/7kche38csQACBawmkCmz1lQ72ocxLTZiUE6kRFDrYA0XLSYh/zxbYt9a/ljESbhSRHR4AzEcAgbsI3NovdbDvwjrNzWfXVx9tmA72RxO/8XkpJ1JlPnuLRM8xxb9nbwC3CoaeUcIqIlsMIIAAAscI3Novuwts9ZUO9qGMSU0YHexD4bLOTSEd3eGQEHsJ7OFxk4MEiOyD4NyGAALRBOgF/8bNzAmggz2Jd1JOpAo3e4tEzzHFvwR2z/j9aKuI7I8m7vMQQGB1AqkCW32lg30od1MTRgf7ULisc1NIR3c4JMReAnt43OROAkT2nQDdjgACUQToBR3smQNeB3sS76ScSBVu9haJnmOKfwnsnvF7lVVE9lXkfS4CCKxGIFVgq690sA/lamrC6GAfCpd1bgrp6A6HhNhLYA+Pm5xEgMg+CaTHIIBAawL0gg72zAGugz2Jd1JOpAo3e4tEzzHFvwR2z/i92ioi+2oP+HwEEJidQKrAVl/pYB/KzdSE0cE+FC7r3BTS0R0OCbGXwB4eNzmRAIF9IkyPQgCBlgToBR3smQNbB3sS76ScSBVu9haJnmOKfwnsnvF7pVXE9ZX0fTYCCKxCIFVgq690sA/laGrC6GAfCpd1bgrp6A6HhNhLYA+Pm5xAgLg+AaJHIIBABAF6QQd75kDXwZ7EOyknUoWbvUWi55jiXwK7Z/xeYRVxfQV1n4kAAqsSSBXY6isd7EM5m5owOtiHwmWdm0I6usMhIfYS2MPjJncQIK7vgOdWBBCIJEAv6GDPHPg62JN4J+VEqnCzt0j0HFP8S2D3jN+PtIq4/kjaPgsBBLoQSBXY6isd7EM5nJowOtiHwmWdm0I6usMhIfYS2MPjJgcIENcHoLkFAQQQ+IkAvaCDPXMi6GBP4p2UE6nCzd4i0XNM8S+B3TN+P8Iq4vojKPsMBBDoSiBVYKuvdLAP5XRqwuhgHwqXdW4K6egOh4TYe7bA/vFPfxwITdYl8OOff96PxPW6vvXmCCAwBwF6QQd7jkh8/y10sN/n8uFXU06kCix7i0TPMcW/ZwvsntGQZ9Wtwu+ZBHGdFw8sRgCB8wncWmc/f//d+R820RPVVzrYh8IxNWF0sA+Fyzo3hXR0h0NC7CWwh8dNXhG4tY8R168gmSKAAAJ3ELi1znYX2Cl6YfX6Sgf7juQ+89aUE6lixt4i0XNM8e/qG0DP6LveqvcKP+L6er94AwQQ6EPgvXX22bruAlt9pYN9KItTEyblRGoERUiHk71+R2jEgEkMgbf7GHEd43qGIoDABxF4u87Wx3YX2Cl6YfUGhg52ZeTFY8qJVGFmb5HoOab4d/UNoGf0XW/V68KPuL7eH94AAQT6EXi9zr62rrvAVl/pYL+O96+epyZMyonUCAQd7IGi5STEvwR2y+i926jax4jru1F6AAIIIPAugVpn3/5ld4GdohdWr690sN9m5kVfp5xIFV72FomeY4p/V98Aekbf9VY9F37E9fV+8AYIINCXQKrAVl/pYB/K6tSESTmRGkER0uFkr9/BHjFgEkPg+f8z/+YP38bYy1AEEEDgownQC+qrj465PZ+ng72H1gO/N+VEqhCyt0j0HFP8q4PdM35ZhQACCCAwN4FUga2+0sE+lJmpCaODfShc1rlJx34dX+14UwJ7ByzfigACCCCAwEkE6AUd7JNC6SGP0cF+CNb9D005kSoy7C0SPccU/xLYPeOXVQgggAACcxNIFdjqKx3sQ5mZmjA62IfCZZ2bdLDX8dWONyWwd8DyrQgggAACCJxEgF7QwT4plB7yGB3sh2Dd/9CUE6kiw94i0XNM8S+B3TN+WYUAAgggMDeBVIGtvtLBPpSZqQmjg30oXNa5SQd7HV/teFMCewcs34oAAggggMBJBOgFHeyTQukhj9HBfgjW/Q9NOZEqMuwtEj3HFP8S2D3jl1UIIIAAAnMTSBXY6isd7EOZmZowOtiHwmWdm3Sw1/HVjjclsHfA8q0IIIAAAgicRIBe0ME+KZQe8hgd7Idg3f/QlBOpIsPeItFzTPEvgd0zflOtulWwpvJIsfvzD2t0hPb6Qzy/EEvz7+fvv9sbKkt9v/pqjfWKwJ4lrXQ4Z/HEY96Dfx/D9eKnEtgXO8DHn0qAIDkV5zIPSxNgyzjmpBdN8293gZ3yE6+r11fLCOz/+svfPn358uXT09OTEQdxIA+mWAduCZKuBc1J9Z7HTErgVjxP+rpe6yQCXdcr8fwSIGn+pRd66KRb+btKPC8jsJ+BEtc9koYf+bHLYdn//vbX75a4q2wA7768i7EEbhU0sUBCDO+6XonnlwBO8y+90KMZuXp9tY7A9jsVrbb6lN8hKaext0j0Glf/EaZe3mDNvQQIknsJrnl/mgBb00vH3zrNv91/RDylnly9viKwj69Z597pd3TP5Tnb0/h3No+c8j6rbwCnQPCQNgQI7Dau3GVImgDbBafBN6f5t7vA9jvY/pGzQ8vSrQ2+e8KknEhVULC3SPQcU/xLYPeM31Sr7L//aO36tPUqLZ759yV96YUey9jq8ayDPUsc6nDO4onHvAf/PobrxU9dfQO4GJ+Pn4xAmiAZ+EPW57T1Ki2e+fclo7sLbB1sHeyxd+2ZpC2IxSal48fe3h2SNP+mFTTlX2NPAvbf3utz2nqVFs/8+7IudxfYKXph9XjWwZ6lTgo5QR+42TtQtJyE+Hf1DaBl7DHqMIE0QTJAWa8Gik6TtHhO24/S/Dty03o1UMw8IbAn8U7KiVThZm+R6Dmm+DetoOkZrawqAqkFq/VqjR+5rDj92jEtntP2ozT/Vtxbr9ZYrwjsitirx5ATqYGZvQNFy0mIf9MKmpaxyqhBILVg9TuNaxSsI1C/cpIWz2n7UZp/R9irrwaKmScE9iTeSTmRKtzsLRI9xxT/phU0PaOVVUUgtWC1XhHYlQMrj2n7kfXKvxkxc74S2LN4J+REauBm70DRchLi37SCpmWsMmoQSC1YdbAJ7JEEC0/S9iPr1d8Xjtb//OqrxzOB/Z99/CHfkXKCXjDZWyR6jin+XX0D6Bl9rDpKILVgtV4R2EdzZqb70vYj65UO9kz59/ZdCOy3RK76OqTjN/Cyd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTtdlBPbMEL0bAggg8JrA5x96FqyvbTTvR+BWwdrPUha9JtB1vRLPL17m39fRbr46gVXimcBePdK8PwIITEdglQ1gOnBe6FICBMml+C/78K7rlXh+CSn+vSy1fPADCKwSzwT2A5zvkQggkE1glQ0g20usf0uAIHlLJOPrruuVeH6JX/7NyOMUK1eJZwI7JSLZiQACH0ZglQ3gw4D4oCUIECRLuOn0l+y6Xonnl1Dh39NTxgMvJLBKPBPYFwaJj0YAgZ4EVtkAetJn1VECBMlRcmvf13W9Es8vccm/a+ent/93AqvEM4H9737zFQIIIHA3gVU2gLsN9YBWBAiSVu78amO6rlfi+SUE+PerU8E3LkBglXieTmAv4FuviAACCCCAAAIIIIAAAggggMCGAIG9QeICAggggAACCCCAAAIIIIAAAvsJENj7mbkDAQQQQAABBBBAAAEEEEAAgQ0BAnuDxAUEEEAAAQQQQAABBBBAAAEE9hMgsPczcwcCCCCAAAIIIIAAAggggAACGwIE9gaJCwgggAACCCCAAAIIIIAAAgjsJ0Bg72fmDgQQQAABBBBAAAEEEEAAAQQ2BAjsDRIXEEAAAQQQQAABBBBAAAEEENhPgMDez8wdCCCAAAIIIIAAAggggAACCGwIENgbJC4ggAACCCCAAAIIIIAAAgggsJ8Agb2fmTsQQAABBBBAAAEEEEAAAQQQ2BAgsDdIXEAAAQQQQAABBBBAAAEEEEBgPwECez8zdyCAAAIIIIAAAggggAACCCCwIUBgb5C4gAACCCCAAAIIIIAAAggggMB+AgT2fmbuQAABBBBAAAEEEEAAAQQQQGBDgMDeIHEBAQQQQAABBBBAAAEEEEAAgf0ECOz9zNyBAAIIIIAAAggggAACCCCAwIYAgb1B4gICCCCAAAIIIIAAAggggAAC+wkQ2PuZuQMBBBBAAAEEEEAAAQQQQACBDQECe4PEBQQQQAABBBBAAAEEEEAAAQT2EyCw9zNzBwIIIIAAAggggAACCCCAAAIbAgT2BokLCCCAAAIIIIAAAggggAACCOwnQGDvZ+YOBBBAAAEEEEAAAQQQQAABBDYECOwNEhcQQAABBBBAAAEEEEAAAQQQ2E+AwN7PzB0IIIAAAggggAACCCCAAAIIbAgQ2BskLiCAAAIIIIAAAggggAACCCCwnwCBvZ+ZOxBAAAEEEEAAAQQQQAABBBDYECCwN0hcQAABBBBAAAEEEEAAAQQQQGA/AQJ7PzN3IIAAAggggAACCCCAAAIIILAhQGBvkLiAAAIIIIAAAggggAACCCCAwH4CBPZ+Zu5AAAEEEEAAAQQQQAABBBBAYEOAwN4gcQEBBBBAAAEEEEAAAQQQQACB/QQI7P3M3IEAAggggAACCCCAAAIIIIDAhgCBvUHiAgIIIIAAAggggAACCCCAAAL7CRDY+5m5AwEEEEAAAQQQQAABBBBAAIENAQJ7g8QFBBBAAAEEEEAAAQQQQAABBPYTILD3M3MHAggggAACCCCAAAIIIIAAAhsCBPYGiQsIIIAAAggggAACCCCAAAII7CdAYO9n5g4EEEAAAQQQQAABBBBAAAEENgQI7A0SFxBAAAEEEEAAAQQQQAABBBDYT4DA3s/MHQgggAACCCCAAAIIIIAAAghsCBDYGyQuIIAAAggggAACCCCAAAIIILCfwP8DgObxIIK3MuAAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\" width=\"246\" height=\"75\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call an integer rectangle as \"squarable\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003enon-unit squares of equal sizes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle can be broken into six \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e squares. Therefore, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle is squarable.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 88.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 44.25px; text-align: left; transform-origin: 384px 44.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 293px;height: 83px\" 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\" data-image-state=\"image-loaded\" width=\"293\" height=\"83\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInteger rectangles that are not squarable are called \"non-squarable\". The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.5px 8px; transform-origin: 118.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32.5px; height: 18px;\" width=\"32.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e square units are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 774px; height: 18.5px;\" width=\"774\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 47.5px; height: 18px;\" width=\"47.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the program should output:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABTgAAAAkCAYAAACtxVW8AAAXPUlEQVR4nO2da3XrMBCEh0MYhEAIFEERlEEZlEEpFEMhhEMpFEMp3PvDneONqpftlS0l852TP23seGVpVzt6AUIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIsRdPGz/n/R+5yBOAVwDvAK4A/h30DKcDfvdRuRz9ACs5Y25Lo9YX2nAP7yD8vAJ4Oe7RVnMB8Abg4/fzfOzjJLmgPtaMVr/WPC/LYzRbY2yx4RHtP2Gu66Nzwva+Ya/9yxqW2n9vMeiMcn/mnn1/jf0ho9qa4hlTH+QTUy42ml2K39uvH7kcljy7jd3h5xlT/R+Zre9xqS+w5Sf6hfW+Sy6YxD9+fjAJglcA38H/Un/vsQP6hKkx2Wffk5ff3+32xd8RL5jq5OfRD7KQZ/xtS6yrPbapGG/4a8MPpoRsJDgIEvv8YBzh+YTbd/KG/utSrA2kPqN0Ep8w1amfyu/zvf1gsvENc6ztVZjOsdR+r2t7YWlMegbwhXh9H8X3EFuXt8SBd0xlMFosWWv/vcSgM6YBtX8oJ7H36PuX2A9M7/UdU1m8YY7f3xiv7gOz/T+YbRil7pJHj98eOdUzpjYwWl4GrLPf6g2xz6hawJb+2FJfwN/6wuwLPzFuX+jeOWF6t/8wvefueMXshMJE2Ha4ws4FBbyv1g+4gTPm53/b8XdPmDtuo426j0QoEI4USJm85RKa3oUpduI/MM8UpLPbu81t4Qn5dzGKHRfM7WEUkZyd4NpP753EC27jZk2n8IRZ3AqTIdu5G4E19ntc2wtrYhL7UldMvoZix1GDs1tgks9nXyvQWJ88ksiz1v57iEEnzH0CfnIC3735/qX2A1OM/sLU3sPknb7/Gvlfr7xgrv8jChKPHr+9ciorfIyUl62139ob+4wUw8nW/thSX/CCdFuxfaTRfMo9E/ZbuuMT8cZ3wu2Dx0ahvtC342aj2LtzZEdyei6fkXnHlDxQoB8pkNIpfGAWoU6YRw1pT8+DBxyhDjvwtrM3yqyTK8apOymsrxspseCqgJwYy1j0vcsTrecVU7t4xtyxq+kUMgmK1UHbce59Jsha+7de2wtrYtIT0rN8rFjSu7hzxmT/C26fe404GSaLIwicW+0fPQZx+WE4Ezkn8N2T719jP8x3YwK2bQcjCNy23o84sePR47dnTmWFsVH82hb7Oet6lH53ia39saW+gJPRchN72M5G9C33zDum99ble/mHeKMMR1djXOHjtC9oM73VNrK9sLNGexep7oXWgZSCtdf9v5Cu72Fy57V/DTscHskiRcxUMLdim+f+O542EG7RsVfns0W52FG0PUY4vWw4o65TmBvZXQPLq6WAxrpa+g377lJ1kHHMqwPdk/3e19bg7c9j1Mak2CARsX0JT5/X2v6tsy8p9rUSOFvEEctS+/eOQa3ttwP8ubp9hO8H2sRgS439QF0/yeYwXnG9hf17TuroKX4dEb97il8xKPZRvPd+zh7t59YE98jS/tgaX0BROfcbe7x30YZWGl+WM9Kqq11Cm5pe7dGgKZa0qLScDbdngwj3KL2nUZ1eGUng5DLiXJ2wbc8rCfFMariJegrbAfVcJt0iMWPnc6/DLLyTCyuI77WtgafAWTMzjWKH1yy2nhKkT5TfnU2EPUSQnuz3vraGXhIkztqvuY+n+NWzwPmKKT62EneB/gTOvWNQLwLnEb4f6EfgtL4/hfX9XrM4ve239X2PCR09xa8j4ncv8SsGB2u4l+IjCJx8v68Y+0ClFEv6Y2t9gfWZqdyY3+lyr0eRpKXGtxq7zKLV8gjuP/MP/tNbW3aQU7Bxh7M4JXC2ZSSB8xnl+thi/7HWSY2FAd/7fXjbELZTDki0PJjHO7mwMzz2GkFunSBauETRc7uDXhIkuw1MbgmmPQjQo3PXi/0trq2htwQpBf2T9yBprwKnTY6x8h419CRwHhGDehA4a2jh+4F+BM6apZ+2Lnm1V2/77YSOPWYh9xK/jorfvcYvnj1BveBRBM7YIasfuB+xc0l/bK0vsCuGU20ktc+t6JeWGt9qwv03lzZUzvBKXXfC1LmyS3GfC9fwuvA7qZHgVstkc3xjFhmsQLykQV4Qty/XwWO5LBnl5n1tJzr87VEYSeCswXZqvWYu7Clwchazd13ytiE8ECD8tCgrT58U+mm2ZfrfUUTaHPTjnqO2vSRIS5LXmkSqll7sb3FtDb0lSCn4nN4d+h4FTo7y28H0RxA4j4hBowicLXw/0I/AaQWRFOfK7y3B034rTNjYxHykxeSOXuLXUfG71/j1gdvVno8gcFqdIfb5wPgTnGr7Y1t9gRVHU4datzysKaaj1OTfa/SXFlwQz/m4P3RuouI5ci3zyPC90V7el3tph99ZovGdg/+dEt9zwVbU2iDCNfY/mE8C/cFkePjiebCRNZ6FFDPqyXyf9+b3U06IHce9Dirg6ZmsDLV7SNG2mCBa2ibg5fe6L/PdkrDEg2yYTHxifldLO71sAFs/W7k3gZPO3HPmzl4C5wfmJYbetNqD8wnTO7ZtMBVot+KZXNjN0DlyHp7k+A3/d76nwEk/6iny9JIgLdnM3r7TrT6hF/tbXFtDTwlSCp5A2mK2Qo8CJ/t0tm4/gsAJ7B+DRhE4W/h+oD+Bs+TTexY4bZ7zibhg/wXf5L+X+HVU/O4xfvH0cVunHkHgBGZx5hW37cHm7mveeS/59dLtGtb6ggtu85cvTGXL990qXp1wW1eph1BbSWF1qXdM9n5g7su01gvOv79n+wyxsqVwbDWkV8zPGcaDJ9yKzeF5G9xayV4b9lFqNT5u2cd7UEO0kwXdsRWz5iVRXAu/S6HmB/FgWtOBS927tE8hC20PUYr74NnnWLrRrrXnhFkospWMpKb9ssLFfs824rC8lpz6aLEVfO3Ho5OyNZkssbfAyfbnuTVE66QmPD30G/4jWnuItE/4m2T2uv9X2Jn6wDxKxoGMFkly6wSRtFqi2EuCZGPEkgRpa7n3Yn+La2voLUGyXHDbrsN+hQe9CZw8qTWs10vusYTeBM7Y9S1j0AgCZyvfD7SPX7X22/5zTsT17Cvb+3nYHw6ovmEWVsIBVy+hupf4dVT87i1+nRE/RflRBM6QM/72zdfkcr3k17X9MQ9fEIqczCVb7k3NfNuuFLhE/ha75hO38YkCXe5ab9hXiL2fVF/kgviMWw6sv+C2Dsfe11vh/zD/T+WfzFGt73iN/M0VmxjnOkFcVpRzBDb5ttiCL50+F7u3Ldyw8u+9/yZVdIutPDWb7VLg/ML0zLyGSjk7uNYBhLal/m7fU6w86MCWLp+wM2nXfjyC1JZgVMOeAifFcs/Zm0C7pIajSOFojXenFth3mb0d5PFcFuGZXNgkOFYmJ6zfKiNH6wSRtFqi2GOCVKrTsZHWtfRif4tra+g1QWI8tf2vUgdxDT0JnIx3sc5sqz5c7wInaRWDRhA4W/l+oH38qrW/ZgZgz0vUa7YyCwULjz5tL/HrqPjdW/y6It5OH1XgJHb5+pqBml7y65q24OkLYiLnFe233ArrMFfGWk6Yhb+SLrXXXqG5umr7EOE7se/sDfMsbL6XnMYG3AqgMUoan/2/7f+dMtdsJtz0PFepbMVPVdaUyGdnLMbgi0mJbu+Z/1vH0vpUSr6k8GXYjaVrxCoKERwBiH2fmzjHKjMrY+iErMhR2rx31NPJtgYju4dG7MO6eC18z6Ou8T0unbHBZRKpD9/xe+F7Hstfw5mctffsxQZiR8Zq71laVmId+tZlJbbzlKp7dqClNkne04YcW5Yo5p6LieVP4XtbEpGlCVJphH/pLPsR7G9xLdCHP98ak2KzQGrfx9H2Wx9Rk/iXBseXCnFHx5El9pdYE4OOtt9D4Nzi+4+OX7X22/58ylaboNaeSryX/fZeuWezuV7tTLYR4ler+H20/4Z51lL8ekO6j79W4BzJ/hK27m/xKUdS0xa8fAEFxG/8XeKey3O2QB/8Hdz/BX/bakmXss+8B1Znik1syx1kZ3NDrqKx9jMGp94n753KK0san9Uaw5mwzZanW3Ew9RKB29HHVCfOKsRhIdHhxwonLPgYtpMWwheTe34vrpj3lUh1JP6hfEiQLfNUeabU+NxWAOHS99xvj3o62dZgFL6rtZ+tyQyd1Zqp2bazteXjNauhtC/ICDZYX1h7zz2XldR+336vJmntYWnM1iWKHvVoS+f26CVuI9jf4lqgD3/uUYbAenHgSPtrBb5X5AfA1j7H0XHEU+BcE4OOtn+rwLnV9x8dv5bYb/cg+/f77PYMAzvIUTsBYS/7bT3P+Tn7vdpBVo/6O2r8Ptp/2+fN2cV8JWXPWoFzFPtr2Hs1aQuWCpxrfQEnY30jvR9kiy1LbDvOHQpldalUneez7rWdndXhQvG35J/Yt+R+o6HuQFti/U4rrKb6pTmNj9hYtUv7sCJaKqCWlGFiK4QVIsOpsSEs2JRybJ1GTJTbaw8Edj5T08Nr958Jp7LHsBWKlfUJcwV5w9+GacsppYjb3x71tLetweiC/DR/1sefwve2CMQczV87csGtDEp18bvwPa8RMtv2ax1XbzZYP1WbqJWWlfB+X5nv1NbjGh+M4Hdr7NjThhT0S2t9eO75rfie+96WPXA9O4VAOT7Efr93+1tcC/Thz70SJOuDau91tP01At/F/L8008zONKzx7UfHEU+Bc00MOtr+rQLnVt9/dPxaaj8PbeBWP5+/9zjjdoCjtj3uZX8sJ0lxj/GrVfw+2n/b503ZxXzlA+WZ4lfzt5r2MIL9S8htDzcCNW3Bwxfwd3Jb7LXQdcKZ9KntvkripWfcryU1mc9qdKnnsTaHZWrfZ2yCUinGlTS+2O9wRn5TakS5F/OdmgOCwkLKKeH23i+J+1oRNhTlbIGlrveAFShnf+1J6h8V3wuXqjC4vCAtTNprUp3Vkpico5dT3jyDUYzWe77QgTeblo108GiJt7M/0gYv0XRL4hdiOx65wQmb1Hj8rue9UvCZW8wqZ0fk6D28wiUaOazv30ov9re4toZR9vAiLA+v5+1hD861sww9fH/rOOKd6HjHoNb2bxU4W/p+oH388liiD9wmqbmZzktp0Re4Vn7Pw6f3Er+Oit89xK+1syw9nrkH+5fAurRUj+glv67tj23xBRfzt1icswJji1mcVjcK9SrgVpdKlanNs1pvjUhSk/nC/lXunJqYjma3AYlRqhM1s13D32Kca1Z24UuuEc5SnRAbnEOnzutjhWNFwdjv2xcTa0i5KbuesALlGlrtSeo1M7FyJ2WV7psKqrbRjnzKm2cwitEyoO4hbgLHioNeicTeNnAUynOrC88ysQNINae1enUMWieI9PEtOjJAPwkScNtpSxHOZttKT/Z7X1vDqAmSl9/rQeAszTK0fQs709BD9BpJ4GwRg3oWOFv7fqB9/PISOO19PCdreNpfm5fUih819BS/jojfPcSv0izLK27zWo9ZtaQH+5fANrJUj+glv65tC1t8QeoMEYvVdlr4bnv/0E8tOVDHYxCjBqvX2X4Rl/XzvcX6DqUtJnMHKcFcm/p/TuOLYcvXw0dEyb1gi214qU6IvVeoeOem+pZEOfvbtftvejcGdsJKwcoKiCl7bCXN3W9p4yndN5zCvCZx6OWUt5EFzhpxc4SkLoRtxNPZ720D26+n+OwZoGtnq2+ZpR2jdYLI2NFqi5GeEqTSSYWAf8euJ/u9r61htATpG74b7PcgcNbgJRKGjCRwtohBPQucrX0/MIbAuWTJ51I87a+ZUFKzVdYSeopfR8TvUeKX98oDMor9wLY8qJf8urYtbPEFNQKnjatb29EFcV9kl21bbSunS4VL3JsJdAG2vPmsfBYbP2KxtDSRMJdXPhX+D+Q1vpfIdbZeNBOIa1XUmlmWrBBhJyq26e4Vc4PIGfkR/PYz5lO3+Bz8XVbeZ/g7Qj5DaYTZVoTUEpPazpBtYKnffcdcjrlRQ84aDN/jBWOepD6qwMk9l3K8wOed7C0Ossw8l5l521DaE+gb/lPmvZMrjpqmgoLdC8VrFkjrBJE2tdpipKcEyQ40lTbr9vI/PdnvfW0NIyVIfFeeApcEzn4EziNiUM8CZ2vfD/QvcNqE+Qr/maye9tv+RcpH2eWKHvW4p/h1RPweJX49gsDJZeQpOJOt+d6CDVnSFtb6gkvi77FrPVYzPCOuyVjfbUnpUtRS7MS71Lt+wRRzvfw59Ztr8Dfua27zPj4nfztXv8N3xGtJOKgT/r+k8b0nfpdlmNJENpWfrZwlYcLOTAyDpN0QNtaBsteeMTkA+z07zZkFcsIsbobXf5nrwym7F+QFwTWw4tSITuGS/1jDpb2lRpvbp5N22r/b92k7SbbMeM+v33vETmEfgREFTpb9++/9Yx/P4OiZ1NAB/iTu12LWCeBrgxX3P/G3bX5gss97HzDv5Ko0msa667E0jLRMEO0SxVZbjPSUIAG3HbcwVj2Z/3mVR2/2e15bQy8Jkh0Ifkd8P3Eu7/Psw0jg7EPgPCoG9Spw7uH7gb4FTnuqup244Ym3/aVZjKxvXjObeotfe8fvXuJXiXsXOMO9A1Pniew1o68VS9rCFl/A/6W0FcZLj7iVmoDDbb/C925naPI9U0v5QHlJttWtvHIxPhP7jtTIgL+zO6mdAeWc0epC1PNsOV0L/y9pfNy+IqwftbrhqvKzAlrKcItdo29nDX4hfxqSbQCcRWixhrBz/4O50r8F/7eFES7r8BbsmHDUCpxWCY816poRD2KTIdr3hrl8Yp1g+07tngx8t3bUYVRx09aHVhvUegfUsK3lPl7TtT2TGttGWe4UZT/x1+F54WlDuAkzDwx7w9xWWrSHFsnVC2bfwNE6YA5y3olSywSRz+wpyIa0TpDCDfhrBijYpuxI5xOmZ4x1nj2eryf7Pa6tpXWCVBuTwo3erQ/6+L22hQjVek/pULhb63t4j5EEziX2HxWDWtp/xvrlenv4fqBt/Npi/xumOpAaOPaihf0UBmzux6TbW+TpMX7tGb97iV8lRhU4a+2PHbT0gTkv/0a7g9L2Yk1bWOsLTrgVOe0EN97Ty4/wfpzcBdy219ShO7SLYhx1m5IuZK/33iqMMcO2h7AO2+eyZzfE+ibsv7AswlhU+n9J42PZ2Xdsc9UYq8uPokRs/4Y35IXOl+Dad5QbtN2cOPVdLivnPa2DOf/+7wPp4+t5nffMzVj5xJzfk3mO3DX2njUB8ITpRduyKZX3q/mNcHovfz8s4xEI615Yxr12KJ6xbA8Vr6Va3klNWP4M7HucrO25RJ3bBFwxDxq0XE7SKrkKfQPbQQtbWiaI3HeoZcewVYIU1if7qfHVZ9zGjQ/cCtaez9mb/VvLbgmtEqQ1MSnlg1rW/1b2p/o8tGlpPS71E9fSSuBbY/8RMaiF/Wek94wLZ3Ck2MP3A23i1xr7T5hsfcc8mcNzCWOKVvE7jF+sy965RY/xC9gvfvcUv3KwPXjPYOzJ/li7L+kmI+DdFpb4gifclmkLP0IbnnFrZ87/2vphn8dOZMu9dw5ce/ldagkxLYw6WUxDYNmmJtVRo/uM3Df8f6welDQ+3teWp51hmsK7/IQQmAXrkYPWC9onTq25Bxs403W0AQXL6Daw8zX60qG1PLr99+DPt/Do9t9DHNnCo9vfS/w6Y94vrbWoaenF/rUofj22/350+0Vf2BWZQgghhBBCCCGEEEIIMRRcnn49+kGEEEIIIYQQQgghhBBiCfbcl5b7JgshhBBCCCGEEEIIIYQ79sAe7Q0phBBCCCGEEEIIIYQYBp66ToFz1D2NhRBCCCGEEEIIIYQQD8QZ8dPlcyeTCyGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQog/+A5GxrwBypFgAAAAAAElFTkSuQmCC\" style=\"width: 668px; height: 18px;\" width=\"668\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.5px 8px; transform-origin: 247.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Reflections and rotations are not significant and should be counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function TA = nonSquarables(A)\r\n    TA = 8 * A + 8;\r\nend","test_suite":"%%\r\nA = 20;\r\nTA_correct = 168;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 200;\r\nTA_correct = 24732;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 2000;\r\nTA_correct = 3128803;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 20000;\r\nTA_correct = 382868578;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 200000;\r\nTA_correct = 44889840284;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 2000000;\r\nTA_correct = 5150630032283;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nAs = 1000000:100000:5000000;\r\nTAs = arrayfun(@(A) nonSquarables(A),As);\r\nss = floor([TAs(1) TAs(end) sum(TAs) median(TAs) std(TAs)]);\r\nss_correct = [1237846589396 33831082399137 567489801806465 11849294784960 9910963238214];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('nonSquarables.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-23T12:36:30.000Z","updated_at":"2026-03-19T11:13:38.000Z","published_at":"2021-11-23T18:56:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAny integer-sided rectangle can be cut into unit rectangles (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\times1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and rearranged into sets of smaller rectangles. For example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle can be broken as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                      \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"75\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"246\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe call an integer rectangle as \\\"squarable\\\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enon-unit squares of equal sizes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\\\\times6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle can be broken into six \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\\\\times2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e squares. Therefore, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\\\\times6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle is squarable.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"83\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"293\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInteger rectangles that are not squarable are called \\\"non-squarable\\\". The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e square units are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ 1\\\\times1,\\\\ 1\\\\times2,\\\\ 1\\\\times3,\\\\ 1\\\\times5,\\\\ 1\\\\times6,\\\\ 1\\\\times7,\\\\ 1\\\\times10,\\\\ 1\\\\times11,\\\\ 1\\\\times13,\\\\ 1\\\\times14,\\\\ 1\\\\times15,\\\\ 1\\\\times17,\\\\ 1\\\\times19,\\\\ 2\\\\times3,\\\\ 2\\\\times5,\\\\ 2\\\\times7,\\\\ 3\\\\times5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the program should output:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eTotal\\\\ Area = 1+2+3+5+6+7+10+11+13+14+15+17+19+6+10+14+15=168\\\\ sq.\\\\ units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Reflections and rotations are not significant and should be counted only 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Sequences 77: Powers of Fibonacci Numbers","description":"Given integers  and , we are asked to evaluate the following function: . That is,  equals  raised to the power of the -th Fibonacci number. We define  as follows:  and  for .\r\n        Example:     .\r\nPlease reduce the output, modulo .\r\n------------------------\r\nHINT: One solution is already shown, however java math is not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 172px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86px; transform-origin: 407px 86px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 47px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23.5px; text-align: left; transform-origin: 384px 23.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven integers\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following function: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"82\" height=\"25\" style=\"width: 82px; height: 25px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. That is, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equals\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e raised to the power of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eFibonacci number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76\" height=\"20\" style=\"width: 76px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"33.5\" height=\"18\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.5px; text-align: left; transform-origin: 384px 12.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        Example:     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"162\" height=\"25\" style=\"width: 162px; height: 25px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease reduce the output, modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93.5\" height=\"20\" style=\"width: 93.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e One solution is already shown, however java math is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = P(x,n)\r\n    import java.math.BigInteger    \r\n    m = 2178309;   \r\n    p = BigInteger(num2str(x)).modPow(fiboBig(n),BigInteger(num2str(m))).longValue();\r\n\r\n    function f = fiboBig(a)\r\n        if a == 0\r\n            f = BigInteger.ZERO;\r\n        else\r\n            fs = [BigInteger.ONE BigInteger.ONE];\r\n            for i = 3:a\r\n                fs = [fs(2) fs(1).add(fs(2))];\r\n            end\r\n            f = fs(2);\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nx = 3; n = 6;\r\np_correct = 6561;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 10; n = 10;\r\np_correct = 1704349;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 11:20; n = x.*10;\r\np_correct = [1789328 703074 1326793 1022378 1427238 485143 399395 1317366 1490422 632477];\r\nassert(isequal(arrayfun(@(i) P(x(i),n(i)),1:length(x)),p_correct))\r\n%%\r\nx = 50; n = 50;\r\np_correct = 2101373;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 1234; n = 5678;\r\np_correct = 1816441;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 11111; n = 11111;\r\np_correct = 1606418;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 99999999; n1 = 3200055; n2 = 1185207;\r\np_correct = P(x,n1);\r\nassert(isequal(P(x,n2),p_correct))\r\n%%\r\nx = 123456789; n = 123456789;\r\np_correct = 1611366;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 1e12; n = 1e12;\r\np_correct = 1935991;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = setdiff(primes(1000),primes(100)); n = x.^2;\r\np = arrayfun(@(i) P(x(i),n(i)),1:length(x));\r\ns_correct = [828561 675946 113 717102];\r\nassert(isequal(floor([mean(p) median(p) mode(p) std(p)]),s_correct))\r\n%%\r\nfiletext = fileread('P.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2022-10-19T20:51:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-10-19T20:51:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-18T16:04:17.000Z","updated_at":"2026-03-23T13:00:56.000Z","published_at":"2022-10-18T17:04:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven integers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following function: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x,n)=x^{F_n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e raised to the power of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. We define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_1=F_2=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_i=F_{i-1}+F_{i-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u0026gt;2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        Example:     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(3,6)=3^{F_6}=3^8=6561\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease reduce the output, modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{32}=2178309\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e One solution is already shown, however java math is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52809,"title":"Easy Sequences 28: Sum of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the sum of the radicals of all positive integers . \r\nFor , the radicals are: . Therefore, the output should be '41'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAlCAYAAAAQjPROAAAB60lEQVRoge2ZXZGFMAxGjwccYAADKEABDnCAg2sBDSvhesDC1YCF3YeSuR2gf0BbdqZnJo806UfaNC0UCoWEjAZrcwZ1gRbznIL5BWbgvbH+jkgz0LOfy4yaZzC//N8s8aUloTj1+k0LVGecBlJp/rbWAS/H90nE6YDP+o1ub5RgsRgPfOrmij+6OC9HgAtxBKrWsU1+3x5jRBVHBp/4ClChNj89k+YzATgYVx9Xlm9UcWaUMEds/2xzJggLC+49xUU0cRrcf05fcsOZIAz02phXRI8mTod7wuL8bnG2m/+CyuBQoZKWcpPzO89MkjUmm/Dfh7KKIxO5unFukfPUAPxwXKl8/GUVZ1rHOdW/BFCzF8nHZzZxpFrdnTU29CW3ePjNJo6cXlP3Z3qFzH5CPqJZv8/Rwdf4V8jk4lSopXT1gHYFuYp4lDgVKrCcwoCqVj6Zm0ycpwgD38xxNbzJxPERpjsTSCCy5/g0u0nEmXBfEfSYm9QQGuxxydnKJ/bo4kgwL8wX2CEB2xj4VqIP+15Kzjm+h86o4sikfeyOOx29V9N7qRGVuR/Clm7Urnx7m2+zu848NSpL9bHHk+Nn7a2eThHHQhHHwiVxBvbvQTGfWmKiv6mJSfULxlR1Yt/NxML2xlUoFAqFJ/MHD+QAbMqdxgIAAAAASUVORK5CYII=\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAkCAYAAAA9+eyvAAAB4ElEQVRoge2YbZGEMAyGHw84wMAaQAEK1gEOcICF1YAEPGDhNGDh7kebocvwkZDu3N1Mn5n+2e3bkJeQFqBQKBQKhU9RA5VR8wCaqPVQxXWs8b3aN2rgBXwTEtMEfgFL1Mj4ihd0h9kQP6cWWBNKk7larIqBF2AAemDcrGE1ozfEz6kFoI2LtKyOahabCOZty/DBWiGT4ToabDcil3YXrasN4e4fIdW1KONWcW5aUdpkPNpDtEa0nDdFWWdWxh0J1ZPeWW0yHu0h7ucsIhXRKeZ2hOZaY0/Goz0lhxFSqhPX25j0E2mqlmQ82ku8RshOMqLby2fCjiNYkvFoL7lrRAU8eT9PTJz3kYGQTGqYNhmPVsUdI2QHmRKtjIV9M5r43zaGJhmPVk2OHrGtjO02Kz1kr5FeJePRmsi1a9SsZiy8l/DI8RnkKhmP1kQuIyA8x9u1OoIxLeHCt6NLNM/k98qpNZPTiL07tNdHNOPh1Jr5hBHpMXsgJHQ00nedOfm9dmrN5DTiGdcZriYmeJ7zP9sjJsLx9+5b5L8wQhrh0QcYeddojfH/hBE1ITFZrD+Zu/2IM8X5PesR+87F/KoRZ43oxf7hRbazdO4Qf/N8s5Td4U6T82gLhUKhUCgUClp+ANDXK1nbeFY7AAAAAElFTkSuQmCC\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.5px 8px; transform-origin: 182.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the sum of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADIAAAAkCAYAAADLsGk3AAABXElEQVRYhe2XbRGDMAyGHw84wEANVMEUzMEc4GAW0ICEecACGrDAfrS5ZT3YoJSP7frc9W5Hdk3eNEkBMplMJpM5FwVwOTqINRRABfR+/RxawODX/dCIFjIloDwyqCX8vIASqNlHQDmyrwEsLpHRm9a8gt9CwM3v+VA+jLdZoFPPWxaK2UOAYHAjW/x0/vkVVwFXoFH22eM9FFCzfQ8Uyl+FC7bjlf1K2WfHYnk/5h53/NH1OQN9IhfvUwcsJ9LGbB6W15aC7spHiysnjfRJtcbJHoJ0Q9eBzSibTeFsStDa/il578kwQTflLymp7xQJdPC/Q6Q/msj9v5LqltejdaxcxRb2TXJCQUtLQAIdy7ieZqX3FTW5liCCum9/VFg+Z1x6Um70lh2/dwrmTzQZu1NlJWXX4xI01kOnQN6xpr5hjLc3RIxem2CdgmHlOs2n7mPl2mzeZzKZzH/wBNgaraIIzz2QAAAAAElFTkSuQmCC\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e'41'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumRadicals(n)\r\n    s = 41;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 41;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 3512;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 351964;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nns = 1000:5000;\r\nss = arrayfun(@(n) sumRadicals(n),ns);\r\nss_correct = [14572533416 1407530 2206262 3168720 4321316 5635156 7128944 8813000 2478567];\r\nassert(isequal([sum(ss) ss(1000:500:4000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 35252550;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 3522204030;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 352218412502;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nfiletext = fileread('sumRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:12.000Z","updated_at":"2025-12-22T17:26:46.000Z","published_at":"2021-09-27T10:53:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the sum of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'41'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52814,"title":"Easy Sequences 27: Product of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the product of the radicals of all positive integers . Since, the radical product can get huge fast, please output only the number of digits of the product.\r\nFor , the radicals are: , their product is . Therefore, the output should be '6' digits","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABq0lEQVRYhe2XXZWEMAxGrwcc1AAGUIACHIyDcTAW0IAEPGABDViYfaA5W5gG+rdnH6bfOXkYpgm5pUkAqqqqqr5RBmgifTprbaRf6/iebbS5JMnYAO/ApBpnvWsb8Aj03zz+YnNc+npSdzDmJpE38LqJ8bzx72JBehu0B5YImBlYgcG51vK5Kb3iL08l5Akmyd2pK5jeJqKtceNMypqHjZFcE3cKhZm43tHGibMpa1b2k9AR32yCFAoT0mVmdJiBz/pY7PViYKEwIRIYX0da0Yt+I6HwfSoJIwlrx7Fjr70XfjitcQSrFIyxMVbCC3zg2Oo3Mo9cKRiJE9t2G47j4ZmRQxEYmR9J05vjME6NAZSBmdh3N+eIyODV2nqQcmEe7HWS2zx6/hlmoAwI7J1OGkiyUmFKgsDvkxlzgqTA9NyDtMS9g0nNZM2aWJiW+4kt7dY4vzt0OJlRWZ0M4mAEZLF+mq2nxNzB+OTY9QR8Cbj/pQzH14qrgSUgVx9W2qvJfPpvtfd62ZgjGW3d2ECzx0b8U3xS1vts8iQ3nGKMFujPvm2qqqqqqqq+Uj8xKNuJDs64CAAAAABJRU5ErkJggg==\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the product of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110px 8px; transform-origin: 110px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATEAAAAlCAYAAAAqVd5RAAAGGElEQVR4nO2d4ZXqIBCFbw92YANpwAqswA7swA5swRq2BHt4LViDLfh+4D2ZZQmQZBhzcL5z8muzgYHJZQYIAo7jOI7jOI7jOI6jymXiOnyyUo7jdI2q7rwA/ANwj66TRk0dx3ESxHpzB/BEELLZvOBRl+M4n+eOD4nYsOJ/azm8L4uydqI8C6xsk3bF1xHAtXH5A4KD3t7XceXzcvakrt3K8mJ69kmyx/x222N5Xc1F7ATgAeBnSaEV7BCc/RVdTwDnBuUdEdLquLwr9F8Aa9uA4BxxefJq8YLs3uU+3mVcEJxcgxPy9sTtqlFuzz4p2WO0s1akpR5wsGK71NbVTMSOGJ3yhTYitkdogJxjakYOfCHYiFf8tvGuWJa1bUBwolyZmvaRAWMb3qEnXiT1cre0r2efJCmRrhEx/k9s/xljXWuEzETEru+KsXKtROyO0GFycWHA3wZem5IAwfbHxLNkeVqRiqVthNFQy9FbIqOkFlHD4f3s0uLTtfK+Gnr2SbzLuuBv9FcSMWrBlH/dUS/w5ulkKxE7Iox4U40n0yKNsu+ZsvaiLI10wdo28kT7OS9CgZkzAs/lhrr+eEAnlezZJ1NIe3IiJiP8Kf+SA1pJELsRsR/kO2cnyn6uLGuH8iitOcJa2kboRGfYLB7QqbXmoVLURFYD9NKunn0yRa2IyYxsqi5SdEsDaTcidkPZ+Rmiar3oU7ADtFKxT9gm51H43BvaCJpMdawivymYSi56KSJ69skUtSIm085c+3BgexTK7UbEaqDDtJjclLAzW414KTRtK63g3aD3IshoRDr1gOBfraKyKSjeVuX25JO1IlYbfd5RJ3ZfJWJ00FZzAkAQgCdsBQzQt437ds4IfRULmda8lUwtHgjOGK/mPdC2zwhTyX8GZZGefLJGxAYsE7Fc3b9GxGQ43WKUHfD7ZW+5dyumtW0sIxYzjZQrfiY3tB4w7iGySjU1U8kaevPJGhGTCzhzRCxX768RMTZwi068YlxKjyMWizmelrbFyFTzifXRmJwfSdV/F93TMpqwTiV788m5IlbSAPm8rxcxrn61nncA0hFLy9U9S9sII5alPiCRgjglHkdxXys7rVPJHn1yroiVbJd+9vUi9oPgnFabNoHfHdAyPfmEbZp7jmpTC83oL4V1KtmjT3o62YgzQkht8cGtRK66tbL1U7YBY4q3VsTk/rAc0qFb2GuZSvbqky1XJ3PP61rEODH8iZccGDuhha1bsW3tpzlyn1QuKmkpYowOLFLJrfTbJ0WMA0atiJU2QHcrYp92FmDsBO2J2y3YxkhsbeQiU5zSaNsqneRm29ap5Bb6rZVPAvUidqu8j/eUBpcuRYwnZuQaaED71EHrGzzJFmzjnJhG5CL3DeWiOo7eLaIlprQt22wL/Qa08UlSK2JyXmyqz6VflAR3syK2Q6j8BfNGrgGhk3J147K97MjDu6wTdEZ6dlRqOXvrtnG3/BQcSVP3LLGNUd2UQMm5nNjp1/YbVz5Ln7awHlvutxItfFJSK2JA+UsFRug1n0ltVsSWnE9EZ/mH6R8U4PEysvHkaltN3eQZUakjY1iPqV3tW7Yt3kEf1437xKacZoltpZGZL0fs8HNty9W3Zu/UlvvtEz4ZM0fEZH3je+WBADUaYypi0sjSLuXUTu4c7KRX5XWM/jf+e65usYPxyBqeTFn6TGbLth0S99/etnHzZG7D6VzbCD+NoZDxRaOo/iD9Ys6xLcWcl2XL/Wbtk6ny5cbaGlFh+8jjivYYI/Pajc0mInZCaKTUL5VMha+D+B+eoJBj6vmpK/VC8CWtnbA+vOskn8nD4Ups3bY9xh3fsp9qj7KZY5uEKY2094K8n821La4r26z2/i33m6VPkpSv8Ko5vy3ucx5fNKcfzdPJJdxh91NwPB3TCrdNB7dND0vbNNi8iPHMdaudzaWD7DRx2/Rw23Swtk2DTYvYgBBKW+2rucHuUD63TQ+3TQdr27RYJWJn/P2dPq39JzuEzrM6UeAEuxDabdPDbdPB2ralxHpzwLjyO5upFRarD2gdx/k+XHccx3Ecx3Ecx3Ecx3Ecx3Ecp2f+A1UUQkRvaqxNAAAAAElFTkSuQmCC\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, their product is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAkCAYAAACDr7TyAAAC+UlEQVRoge2aXbWsMAyFtwccYAADKEABDo4DHGBhNIyE8TAW0ICFuQ9tFqG3LQmlzFn35lurL3OaJuzQ9IcDGIZhGIZhGEYtWgCNon8HoE+0hx+vht8ztNhiO+OLbKXPdJVtkhZO5A9cIiQ0AFZvE2uvSn61DACWRHxHIlJ8K4DJt8XbHsVbYpulwSYaNemAE9IJ+8C9WTX8apgPYlyRTlzn/74EsTXYXoKhgm2WAU74AcAbOvFolv3c7FdD78flZboBMGI/894RWy5u7Blp7A/+LrUltir4rJGI94P8W1rLr4Y3XMJihKU99E1x5Z6REvO80FaFVrwFTpSzi/pZv1I6uBhzsfHSGc4ISmhsFhK8vHM/JbYqNOKNrC8vMeOJAGolbcBx6eZlivcd2O+pmQpvQ/3GC2zVaMSL7cT4wp7bgJT4vRqeNB4zjymXeG5PCSqxVaMVr4d7q2bEkyjdGX0zaVQxwjL6hF54KoUltmpKxRuxX9hXyErlN5NG68oU/P6CXvj1Als1V4jXYL+FD8Wo5fcMtHuMbVa48Ecx5ZKmtVVzlXgtthknuRH5VtLIb2z95cIfXRDkkqa1VXOleFR2JMF8I2kd8ru2/6o8ErTt/Y1Jo9uKWRiTVHg6JJfYqrlSPApoudnvEbTm5hIG7M+hUuFpzBJbNTVmmuT8cVfSpAkD3LosmQU8djrilNiqqbGmSYK5K2mShPF4aW3KVYsn68N3oCW2KqTiNch/zKM3TbJz1PiF9ztBf132EMQzYl8ZUrclBN/9hWWwxFaFVDx+gJ6wF49K0PtgjDN+ednRLN4062dsHyLDRn1CgelCOeaL4k69DCW2Ilrsr6Jyh2K+paXpPfkgVzgBpLNA47fD3u8Hx5+Fwo+suZa6SuJJp+eiy94X8s9aYpuk9QO+Iu2B9NQd4d4g3neC7v9BzvidfB+6dcn5GxLjp1rupr0P4p0h3zyU2P5T9JAdJ4xfxBOFC7hxLw8UHEaN+xlR8JXXMAzDMAzDEPAHvaP26LcvqHsAAAAASUVORK5CYII=\" style=\"width: 54.5px; height: 18px;\" width=\"54.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e6'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = prodRadicals(n)\r\n    r = 6;\r\nend","test_suite":"%%\r\nn = 10;\r\nr_correct = 6;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000;\r\nr_correct = 2263;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nns = 10000:50000;\r\nrs = arrayfun(@(n) prodRadicals(n),ns);\r\nss_correct = [4503407257 70876 91001 111568 132490 153727 175243 196990 47696];\r\nassert(isequal([sum(rs) rs(10000:5000:40000) floor(std(rs))],ss_correct))\r\n%%\r\nn = 1000000;\r\nr_correct = 5238328;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000000000;\r\nr_correct = 8237674403;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = intmax;\r\nr_correct = 18403071064;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nfiletext = fileread('prodRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:14.000Z","updated_at":"2025-12-25T20:09:26.000Z","published_at":"2021-09-27T10:28:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the product of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, their product is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e151,200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57839,"title":"Easy Sequences 104: One-line Code Challenge - GCDs of Sum of Consecutive Cubes","description":"For a natural number, n, the function CC(n) is defined as follows:\r\n                \r\nIn other words, CC(n) is the sum of cubes of all integers from 1 to n.\r\nGiven positive integers x and y, write a function that calculates the value of gcd(CC(x),CC(y)) . For example:\r\n\u003e\u003e CC = @(n) sum((1:n).^3);\r\n  \u003e\u003e gcdCC = @(x,y) gcd(CC(x),CC(y));\r\n  \u003e\u003e gcdCC(5,10)\r\n        ans = 25\r\nThe following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nRegular expressions are not allowed.\r\nOnly 'pure' matlab functions/commands are allowed (no java, no python).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 372.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 186.2px; transform-origin: 407px 186.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a natural number, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43px 8px; transform-origin: 43px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eCC(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAABaCAYAAADpY4c3AAAK9klEQVR4Xu1dx+slRRBe/4B1MZxUPBgOgouC6aLCCgbUg2AWEQ9iOghiZFU8mFARQcwgLGIEBREUAyioFyPKCh4MJ/FkxD9A65P5sH79ZqZ7XqfpeTVQbHgz1dVV31RXV1f37LPNLtPAhmpgnw3tt3XbNLDNwG8g2FgNGPg31vTWcQO/YWBjNWDg31jTW8cN/IaBjdWAgX9jTW8dN/AbBjZWAwb+jTW9ddzAbxiYooFL5OZThQ4TOkDoBKFbhW7vmBwvf/40hWHNew38NbXfZtsA+4NCtwntENortFNot9ClQq+00i0DfyuWmo+cAPfFQq8KfSj0jNCTQtcJnSL0yXxEHZfEwN+KpeYj5+8iyn4d+BEG4fqh+/Mk+fO3+Yhq4G/FFi3IebII+bHQH0K7hL4RQvz/o/MytNAXK2xrwkrzEZLx/lMi0vWdWPD+LwtdK4QQqJnLwp5mTDULQd8RKc4UOrbz+hCK8f7h8vcThWzCOwtTmRCpNfBPF+Lo2B5zANCdQocKPZS60Vz8zPPn0uzy+J4tXXpL6H6hO1T3Ppe/I7/v/v/sNWDgn72JTMBcGjDw59Ks8Z29Bgz8szeRCZhLAwb+XJo1vrPXgIF/9iZKKuAxwm17Uo5xzH6Rx6sVwhn444zX2tPM089F7i9EEFSGVrkM/FXUXq3Ra6Tlp53WAcAbE0t0iPBDzh9Vn8cJYWFs6KpWDGfgT2z1BtixKlOLWqI0ASHXRUKoCMVqMC9dKlFUfQb+ouqeRWPYhPKpA0AIpksWcguKeqB7lQx4GYrH/gb+3GaeJ39WZ2rpUJlZsiQZL+E9QtgHgI0xxcsiDPzzBGcJqVihqduqEYJgFEBx3P4lOq3bMPCX1vi82uvL/tTYigjwfyRUtCLUwD8vMJaWBqHH90LYmcVLb1QpJQ/keFHorAQNMpzCiIJ+oT+XC73t8l4y+KGEC4RSbbBAnPy3EHYvLelitabuU438O7JBKXSLKlPQS0JIuWJUwUuwklJdKvjpSTCRSqFQAAM8nxB6Q6jo8FzgTbtP2sDpC/pqrkRZhIe3d/cUcKfZSn9iwY/9mwcpjbmeEd7yO6HQTc0p+AGkiGWvSgh8dpG8H1ngC8C6fP0CnCP/WAkXCryMoU3AHkcJ8cQIjB4/O3hjZmtlLWMd8IPZZd1bhuEEKTLu3sdKHmKsz4QgGC7f8nVqfgD+B0K5UmfMk5+f4eUKNXqO+wAcHEXixv9HOmDK0fY6PPV8ZSxLhazWhUKYT2xxwlPAD+XgsCIuVSOkeE1IL07Ac+M8F+zswTUmVGp+aA8dvVroiHW0OeEZlAlgZPG92BNYzuJWhghamHc74MxCQCWEu1bRh2Xcs0eo11GFgp+5WHr6Ma+nVxCHFi9S84NO6AlwqkCJmByj3bNCuUaYWmDrK3+osggVoADMVbBI5tocjhUOCr/xWllFDgG/9gahq4AsoOqLGVPzY+dKeX3dHs6oLL44EwCKmFuGyh+qFaBFdAae/1EhRCIrI5gP/O7QElqDgTfva6EDhXSclZqf1gtOEECYpTdXR+jN+ygPa6qxKOQVLvIG2k+zCXV8kU0nf1y/zFvwPgZ+dwFkauUfvL/Osafmp7XEXHXp7ARCH+TEeWxfcstVZNhX/oz5XIt9ZSnHFmc8Bn4eRgT9I4MTO7yn5qdxwTy1O9L4sAPvjUtP2rnbKSRFi/j4jAS68clZ6/e+8oepTjCl7Ext7itMjxY6rWPuWxnuzfgMgR+N/Kqkjp3wpObnKpRG8oVx8GZYBNEbLFjKy8wAa83h0VfSY07D9Cih4aB+PNWWwpynIveVP6APJcuftc4gz+lCVwox6xiyGAd8fCm0JSQeAos75MV2NjU/F/yI97G24PMAANzBQjh8CRfiWKRFmX1C1uA8IWy4wOULowj+dSaDKbYUphiRXV26/+4rfw5xDD6+Mb/rilRtI0QXGIlvEOLiHGx7U2fTLXsGhsCv010pFJyan6s4HKMXmo/WoxBGtG+FHhNiLbtWrM+jExjrTHoRqmEEirn+7F7cGB4hz86t/EHjSWMYTvYBIabkMUfZK/S+0EqVwRD4eQY7FJOiyCk1vxjw60IueI0XhPTndKjYkH4T/LFhYQgAa9+jyx9qVH7q/hNPoQ6vV3dD4Icn5ZVihp+aXwz46cVgQIQ9bp0OMjjw+CGA3iTw6/TnOiNdqpdXyxFio8F2Q8AfMqHwdUyDPwW/GPAT3ODhll9oxYbE8bVSrD595/id2bqa2R70S4elUXPRpYQ9ADTIN+HlwhTB4aZGOTEPnefETHhbyPZQT30fpcjxgoXwZKIg1EaTPb+eUKSY2afm53ZoSqqT59b0eTD9sbWQxZzexZMQC8o9rWR7WI4SMgcK7HrUbYwiosPxIc/vVveFDi8si3XLYFPzc7UXmm/XL2HfghgVGxrTAsBIla5TRdpCtodhYAoHGIX47mGddg210WTPjwf07B6x8V1CY5tSINibQruE+nZPpeanO0Uj+fLyY15DZ4Ew4f2r885jZcvIOuCF4vepUhh4LjzoyCDPkE1Ly+qmoUNstBb43eo+TFSfE3IPF0IcfbMQvPuYklLzczuFmP+9ESD6vAYndPRy8Op3Cw3tZCK/kIlxaZDEtscda0gBh476sW2GPM9QMdRGozx95QBQAg8WAiNMMgCwr4R2CLFMIGRkwPOp+enOwSugxHho55FeqOkLeRgSoY/w6A8LjW1+52riOiFPiKFr3sNROjq0SNyJqTaKAj8fhnfHl/ZQF8NiItRKDK6eeTqdmh9fLBzDMbSZhTH2So1HJyt3lmHV9HGhsZoZ1rz0HomR2OCl2XEEjMqhZxJa2+h5aSNqf7HP82fqQza2iNuxYpt73ylfJF9qNVtHMzGeU0ozUxf/Z7s08KNn8Fy4ck1CObHP/YJlN77TQO2UJhxKqY1I/3V9ieBHvzAx2iOUei/v0k9uwFyn5GG1fP8wYp+b0WH1OpKlgp8jQMrzHwF8HKmX8iCs0t69rz3Mv5A9wVUjpcn2i7e9ZPDDmPAoUZMihZapB3DNAdg+GXRKs0bKFhPY1zshi2fNlg5+n/E3/XfmzWukNHXtfZViOQP/5sKfKc0cVbZDWsVIg8ODbxHSnybybRrKYiUDfxa1zp4pq1dzfoyCm81xUvJOIWwv5El+WkHRBWrratvAv67m2n1OFxlioht6iLCvxwB7H7h9z9UIuf6TycDvM82yfu87jLZmD6Nr8mOEN/DHaK+9Z1OUUafsdc7TtL1yGvi9KrIblqoBA/9SLWv98mrAwO9Vkd2wVA0Y+Jdq2fn0y7fPopqkBv5qqp9lw9ynAOFiDyZGSlUf/Tj1EOHsCjLwZ1dxUw0Q/DjMC+eVultWp3QGaVXs5ea+aQP/FO3ZvYvQgIF/EWa0TqyjAQP/OlqzZ4ppgAVn/HbBvdJyqnP/DfzFzGgNxWgAQEXJAU+tnnqqXN+5SQb+GIvYs0U0oE9n40FdU88T/aVnkmzgL2I+ayRGAyxzTn1kiYE/xir2bBEN8ECo1NsZDfxFzGeNxGgAIHW/tWsxf4xG7dkmNMBzR7GrarfQdiEsUFnM34T5TMgYDfCkNmwkxxEi+Khb30nbU9vQH/+zFd6p2rP7i2iAx7NjW+PYydRThAHPK4T4WVeMKr4zUKfwj77XanuiVWgMWtWAgb9Vy5nc0Row8Eer0Bi0qgEDf6uWM7mjNWDgj1ahMWhVAwb+Vi1nckdrwMAfrUJj0KoG/gVwVXF598KWpAAAAABJRU5ErkJggg==\" style=\"width: 95.5px; height: 45px;\" width=\"95.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn other words, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eCC(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the sum of cubes of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140px 8px; transform-origin: 140px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, write a function that calculates the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 64px 8.5px; transform-origin: 64px 8.5px; \"\u003egcd(CC(x),CC(y))\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47px 8px; transform-origin: 47px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e . For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; CC = @(n) sum((1:n).^3);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; gcdCC = @(x,y) gcd(CC(x),CC(y));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; gcdCC(5,10)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        ans = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 116.5px 8px; transform-origin: 116.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function g = gcdCC(x,y)\r\n    g = gcd(sum((1:x).^3),sum((1:y).^3))","test_suite":"%%\r\nx = 5; y = 10;\r\ng_correct = 25;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = 123; y = 1968;\r\ng_correct = 60516;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = [123 456 789]; y = [987 654 321];\r\ns_correct = 18;\r\nassert(isequal(mean(gcdCC(x,y)),s_correct))\r\n%%\r\nx = 2000; y = 7337;\r\ng_correct = 4004001;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = [11111 22222 33333 44444]; y = [66666 77777 88888 99999];\r\ns_correct = 112466886431;\r\nassert(isequal(sum(gcdCC(x,y)),s_correct))\r\n%%\r\nx = primes(100000); y = x * 2 + 1;\r\ns_correct = 7455917221644;\r\nassert(isequal(sum(gcdCC(x,y)),s_correct))\r\n%%\r\nx = 123456789; y = 987654321;\r\ng_correct = 81;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = 1:10000; y = x * 3 - 4;\r\ng = gcdCC(x,y);\r\ns_correct = [87238 174316 261586 349208 435182 522452 610074 697344 783270 870508];\r\nassert(isequal(arrayfun(@(i) sum(g(1:i)),1000:1000:10000),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nx = [234567891 345678912 456789123]; y = [876543219 765432198 654321987];\r\ng = gcdCC(x,y);\r\ns_correct = [175689 135837 -96957];\r\n[sum(g) diff(g)]\r\nassert(isequal([sum(g) diff(g)],s_correct))\r\n%%\r\nfiletext = fileread('gcdCC.m');\r\nnot_allowed = contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regex') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\ndeblank(strtrim(splitlines(filetext)))\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-28T12:01:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-27T11:07:50.000Z","updated_at":"2025-04-24T23:46:15.000Z","published_at":"2023-03-28T11:58:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a natural number, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCC(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eCC(n) = \\\\sum_{i=1}^n i^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn other words, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCC(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the sum of cubes of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that calculates the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(CC(x),CC(y))\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e CC = @(n) sum((1:n).^3);\\n  \u003e\u003e gcdCC = @(x,y) gcd(CC(x),CC(y));\\n  \u003e\u003e gcdCC(5,10)\\n        ans = 25]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57805,"title":"Easy Sequences 105: One-line Code Challenge - IPv4 Address Validation","description":"The Internet Protocol version 4 (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\r\nIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\r\nFor example, the following are valid IPv4 address:\r\n    '123.123.123.123'\r\n    '0.255.001.010'\r\nBut the following are invalid addresses:\r\n    '0123.123.123.123'\r\n    '123. 23.123.123'\r\n    '123.123'\r\n    '123,123.123.123'\r\n    'abc.123.123.123'\r\n    '123.456.789.111'\r\n    'i like matlab'\r\nThe following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nRegular expressions are allowed.\r\nOnly 'pure' matlab functions/commands are allowed (no java, no python).\r\n---------------\r\nNOTE:\r\nThis would be the last of my one-line challenges.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 603.067px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 301.533px; transform-origin: 407px 301.533px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Internet_Protocol_version_4\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eInternet Protocol version 4\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.5px 8px; transform-origin: 279.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156px 8px; transform-origin: 156px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the following are valid IPv4 address:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 60px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 60px 8.5px; \"\u003e'0.255.001.010'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 8px; transform-origin: 123px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut the following are invalid addresses:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 143.033px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 71.5167px; transform-origin: 404px 71.5167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; tab-size: 4; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 72px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 72px 8.5px; \"\u003e'0123.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123. 23.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 36px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 36px 8.5px; \"\u003e'123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123,123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'abc.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123.456.789.111'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 60px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 60px 8.5px; \"\u003e'i like matlab'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e---------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis would be the last of my one-line challenges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = is_IPv4(s)\r\n    b = all(s\u003e=0 \u0026 s\u003c=255);","test_suite":"%%\r\ns = 'i like matlab';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '123.123.123.123';\r\nb_correct = true;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '123.123...123.123';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'0.255.001.010' '0123.123.123.123' '123. 23.123.123' '123.123' '123,123.123.123' 'abc.123.123.123' '123.456.789.111'};\r\nb_correct = [1 0 0 0 0 0 0];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'75.255.003.4' 'A.B.C.D' '000.000.000.000'};\r\nb_correct = [1 0 1];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '0.00.000.0000';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'1(1.111.111.1)1' '{1.1.1.1}'};\r\nb_correct = [0 0];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'111.222.33.44'};\r\nb_correct = true;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\nn = randi(300,1,4);\r\ns = strjoin(arrayfun(@num2str,n,'uni',0),'.');\r\nb_correct = all(n\u003c=255);\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\nfiletext = fileread('is_IPv4.m');\r\nnot_allowed = contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":6,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-30T11:04:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-03-30T08:54:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T17:19:11.000Z","updated_at":"2025-12-08T10:44:27.000Z","published_at":"2023-03-29T18:51:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Internet_Protocol_version_4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eInternet Protocol version 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the following are valid IPv4 address:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    '123.123.123.123'\\n    '0.255.001.010']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut the following are invalid addresses:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    '0123.123.123.123'\\n    '123. 23.123.123'\\n    '123.123'\\n    '123,123.123.123'\\n    'abc.123.123.123'\\n    '123.456.789.111'\\n    'i like matlab']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e---------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis would be the last of my one-line challenges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53119,"title":"Easy Sequences 53: Greatest Proper Divisor","description":"The greatest proper divisor () of an integer  is the largest integer , such that  and . Furthermore, we define: . \r\nBelow is the set of 's of numbers from  to :\r\n                                .\r\nGiven an integer , create a function that outputs the sum of 's of all integers from  to , inclusive. For , your function should return, .\r\nTIP: Good algorithms for finding GPD's for numbers  to , can be found in Rosetta Code.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe greatest proper divisor (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e) of an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the largest integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37\" height=\"19\" style=\"width: 37px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Furthermore, we define: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79\" height=\"19\" style=\"width: 79px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eBelow is the set of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e's of numbers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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\" width=\"486\" height=\"19\" style=\"width: 486px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, create a function that outputs the sum of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e's of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, inclusive\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAWKADAAQAAAABAAAAJAAAAADbokXeAAAEJElEQVRoBe2YR2hVQRSGnyV2I6JiwYINERtiw4JCjBVduFBQERREEERdiODGbBRELAguJLbYQBQMoiJWJKJiL+jCEizYsCD2GvX7zR0yuZncd1MgeWYOfG9mzjkzb+bcuWfmvUTCi4+Aj4CPgI+Aj4CPgI9AeSJQqzydUrhPV+Y+DPpCA7gIFyAf4shAnFwxa4p+eUBenIH+N580FpQFP+CPgxx0dSBKxmF09TW659j1PTVSNrNqE4jSylx86kVE51SSMbJcfV3b3eWXyroxTP443IFFcA7qwxBYA33AyGQqh03DKgdQvwJn4CyE5Q2KrfA5bKgJ7WMs8im0diy2IboHYHb1eoePVHuhALqr4aUoAk2ofofpRaoStVloTICvlbAmEl3Q/QLt4HSHvUardFs4AVEHWG/sJsAKYlg2ojB27eJbsAY0doWkJb2Vv5bCFGukTtQXgF6n0ZY+VavdmLgJ4L7QIlrQVl419nB5EJsr9YSGKd5cS1M5yx5sZuAyh/JTyDYosKVqkWmtZ0ZoEZ1oH4KH8BvsmJj6E/TtILb0wHMamDvjT+rNYSEoF2nnHgXzBfOpx5UDOL6tBCrzzdnAfLSWl6AfH6VJYwzaTNtBqcKsX+U1iEpDmItLGs2PoM6nQSniC4wFia475gvG/9PE+1A+NP0qUpblO6Nm1gjjq2BO2lRxpT+O58Feg3nLi41Rt1irqDGUapOgqaS+A+aB7pMSO8HfLFTF+lyF1/5YntFOV6PNsa1ZeLYC5d5w/o0a5DpGPWQdiubqpvS5B2LJCrzM03lMPTvU625gvx3Sp1JzIJNV+rsEug+XR3rTSWlTsbpflgH0pSbA96g3sjp3tGw6EFNR2jPpZ5APbSq4gDv0V6zexx1HVxM7iWeEOs6lbYKvP0BSTdKZsF5xBbhzJUx+F2MoHnrTS4grB2fiVTvwVM7VIWfLmKDxjTLPNsSo6xYxKoZfMhcdSKeSOTnsSgW6dnWAkfAQKiqKg+RFYZH8cysuZodOCLkr8G8CuznwQi6Rzaq8RaQxsyPwAXTdKk1mYxhcmtGhN+l0mcOWcO1gcxV7TQcFxBZdT5RCJCbAeiB6Tc5AMqmqW4Q2xm7IAG2ay+AS7epN0M9ldOhGoNPD0mGpOCSVnniY3Zvt8F5s2RXslaDTsxlUV6nFxLaA1vUcchzsRKe8XAB5INFfmidBfXKhG9iijaYrqsZdZBui6nYAJzkcV6MzD+AsdZ2c9p3Y0aXKVeuYgZlznHJWMGOty/b/SltpQL90p8I9kH0JxJZ9eKrTZ9CBEJaJKH6DfJ7BMKjOMpzJ2UFKVn+Hv73ubbTNeu2+0unAHgCRotenrNKLDulwA/RU/3fRVU4/KNqCDshHkA86o7z4CPgI+Aj4CPgI+Aj4CPgI+Aj4CDgi8Bdj8FUOHwhzYgAAAABJRU5ErkJggg==\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, your function should return, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eTIP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e: Good algorithms for finding GPD's for numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, can be found in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://rosettacode.org/wiki/Largest_proper_divisor_of_n\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRosetta Code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"the function s = sumGPDs(n)\r\n    y = x;\r\nend","test_suite":"%%\r\nn = 25;\r\ns_correct = 107;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 1691;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 16507016;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 10000000;\r\ns = arrayfun(@(i) sumGPDs(i),1000000:100000:n);\r\nss = floor([mean(s) median(s) mode(s) std(s)]);\r\nss_correct = [6131600733080 4992760161090 165051503014 4903597092814];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 87654321;\r\ns_correct = 1268119158203109;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 100000000;\r\ns = arrayfun(@(i) sumGPDs(i),10000000:10000000:n);\r\nss = floor([mean(s) median(s) mode(s) std(s)]);\r\nss_correct = [635439507299878 503400239949103 16504975497498 564032070925422];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 123456789;\r\ns_correct = 2515609811020846;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nfiletext = fileread('sumGPDs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-25T04:32:21.000Z","updated_at":"2026-03-19T13:00:12.000Z","published_at":"2021-11-26T07:30:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe greatest proper divisor (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the largest integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\ |\\\\ x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026lt;x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Furthermore, we define: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD(1)= 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBelow is the set of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's of numbers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ 1,\\\\ 1,\\\\ 2,\\\\ 1,\\\\ 3,\\\\ 1,\\\\ 4,\\\\ 3,\\\\ 5,\\\\ 1,\\\\ 6,\\\\ 1,\\\\ 7,\\\\ 5,\\\\ 8,\\\\ 1,\\\\ 9,\\\\ 1,\\\\ 10,\\\\ 7,\\\\ 11,\\\\ 1,\\\\ 12,\\\\ 5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create a function that outputs the sum of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e's of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, inclusive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, your function should return, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e107\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTIP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Good algorithms for finding GPD's for numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, can be found in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://rosettacode.org/wiki/Largest_proper_divisor_of_n\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRosetta Code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52849,"title":"Easy Sequences 34: Modified Pascal's Triangle","description":"Consider the integer triangle below:\r\n                                                                    \r\nIt follows the same rule as Pascal's Triangle, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \r\nGiven a number  find , which is the sum of the n-th row. Hence,  and . \r\nWe could be getting large numbers here, therefore please concatenate the total number of digits with the last 3 digits of  and output a single concatenated integer. For example the , hence the output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 347px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the integer triangle below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 164px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                                                    \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"167\" height=\"158\" style=\"vertical-align: baseline;width: 167px;height: 158px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt follows the same rule as \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pascal's_triangle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePascal's Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e find \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30.5\" height=\"19\" style=\"width: 30.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, which is the sum of the n-th row.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Hence, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"19\" style=\"width: 56.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIAAAAAmCAYAAAAMe5M4AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAgKADAAQAAAABAAAAJgAAAAC36W5BAAAF7UlEQVR4Ae2Za4iWRRTHXy3NrrZpNzVbqZRqEcwKaiOVoiSivlgYIqzah5A1kqgPRUhWJAlFadAdyepDWVFRH8JY6EZkZhfpIgVquZUlpUloSfX72wwMz87Mc3mf13yXOfDfmeecM2dm/s955vJuo5EkMZAYSAwkBhIDiYHEQGIgMdBiBkYR/zWwpKZ+5hDnfTChpngpTIQBvbxucDU4F3QAKzOpnGAfAqX8vwKfg5EBH596AcpVoMtjPBTd62A7OM1jb2dVJ4O/H4xuYhIx7gqHnYTnq+CfDPbx3Af0RcumxIjJKxj7wfiYU8Z2Hs9/AcW/LGOzj0dR+RhsACOsso3LUxj7o+BPoHmfDqpIEe5y42pp/RVoIFvAbDAGTAQ3gD+AbMI4EJLFGJQwU0MOHv2R6DYBGz+UAGqqMf0IntRDm8pYxr0S7AV2ziqrJEAZ7ugiLH2YNAi9vMket2uN/SePzarOp6JsfsoqCpaP4ecSEUsAhbzR+M/XQxvKi4z5LjAX2FWvagKU5c5L1+HOQL70ejQaw9DvAG8E7EPQfw2UAJ2gqGg70eR1ZrBJkJcAWv63gd1A20I7y0YGb+dddgUoxd3QCEs6dOmQJdFgfKJM1Qte7zOiuwhou3gWbAZF5CScngBvghVFGhifPZQ6NGn508rUzqIkriKluYslwM/OCM6k3u08u9V+Hj5yFU5dy5lEJ/Wioq1C45oHQokXimVXop6QwyDXN8Odlxpdr+xStJX6iV4vv1JL8m/gbzDK7zJA24tG/c0yloXmWbq8LcA0afxg2pRdOm37g6H8wMxB8y46j0rcxVYAEfG4/hjR9WQtKPoyL8B3JPgE6JyQJ2fhcB94GqzJc47Y+4xtRsRnsJkqc2f3+BAhSzGISL1MSRfQ3izdLhCT8cb4RczJ2IZT6pywHSwyuqqFDo4SJWxZeYkG08o28vjrDPKWR98KVVPc5SXAXkZ8FXgPTDSjP4dSP+rMBLKHZJwxFPn678Z3MpgO8hILl6jY/mz/UeeM8Wiej8voqjwOq9KoYpumuMtLAI3pF6D9911gSZ1O/RGgg1pIxhqD2sdEq8nNYDl4J+ZY0NZMAiyjjxcK9hNzWx8z1mirm7vo0HQT0M1ABxML3TlD8jIG+fWGHNAfC7aCDUBLWVYWorB9KQmLiFYmtVlXxPkg9SlyCKyFuyIrgOVIPwbNBjoDDDXKWym1HfjE3mVH+IxG9yCl9uoHgLI5K1McxVTqQ8zzZ5Q67ftEP2BJ9v1XDNq/reBuP1n6YrsitN2DzX6VuuKF9rt7jZ/KkOiGYGOVKeeGAqK/3sSsYymPdNNSU5EVoBbufCuACPwe6OdInzyM8jZj0BfZAXR6z8p3RhG7NiqBhJAovv3q5WN9lSwhGW0MmkNZaadbQC3cZRNAZJ9hECKvH8PvQCfmnUDnAp/YFzDGZzQ63ShiojOAEk5yOdD2kycnGwfbf56/a2+nW0At3GUTQPvxEUBXv+UuM05dX5iIkujwFvoa7X38Qnx0ZrBfL9WWysUm+qcVellGmzq2jmZvAe6qV2Ea1ZtcSlO7F18XCKPDh/WZFfCx6g+Nrw5wVUQrgO2ryC1AyalE2wbsQZVq28lmRmznHTuPxSZWiLssSZOciKup3w6ONzr9H2AFWGSen6FcY+qhYpUxXBJyqFk/g3j6ep4DB2rFqXMKhxDsJnCqE3Qe9dBB23Grp/oQYbaAlUBXLZuFu5z6buqLgQabJx047AGbQBH/bLz5KOwY7NKe9XGf1xp//arYbqLtR9za+brlTvQbS06oLHf7w1/J37OdjiZQXwCWgluADmKxUz3mAaKk0mR6BljqVUwjnPp5vt6wKVqzDBxGgHXgWzC82WCR9m9j+wYcE/FJpv+JgU763QFWt6j/O4irf0xVPWy2aFgprMvAFTzoYHanq6yhPocYWvp7a4iVQrSYgR7i60u9pqZ+uomjQ+aSmuKlMAeAAd1rp9TUj66t+qEpSWIgMZAYSAwkBhIDiYHEQGIgMVCUgX8BmpBi34cjpBMAAAAASUVORK5CYII=\" width=\"64\" height=\"19\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWe could be getting large numbers here, therefore please \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003econcatenate the total number of digits with the last 3 digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30.5\" height=\"19\" style=\"width: 30.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and output a single concatenated integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIAAAAAmCAYAAAAMe5M4AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAgKADAAQAAAABAAAAJgAAAAC36W5BAAAH+UlEQVR4Ae2Ze6zPZRzHjzuFiIhcDrlVUqbLREk1mbWsJSl/RKutRUlrbVKMrdVWa5Jaa0ttKK1GstSKCNOGXEKizEEuJSQKoXq/znk+9pzveb7f3/d3HJyzvp/t/Xs+z+fyXD7P7fM9p6AgoywCWQSyCGQRyCKQRSCLQBaBLAJnOAJN1P5cYXwF9TNU7SwT2lVQe/+7ZqrlMWMWr4vQVNgpbBEOCFB/YZXwK5UYaiz5N8JxobdwUAjRNRKGxtVA8nEOi51jTZVzhGuFngJjqspEjAcIVwgNhZUCMdso5CJidrtAHFoK64TPhc3CaVFneX8i/BvBCdUXCpxodAOFJGKhdgltEoyYQLQfv45/rYh/fdXZfKuFuhFdVaoO12D3Cf58jZ8keehQ2PyaiVnjfDmEHwn7XZ0bspFQLmonL045A9kmDBHYXZ2ER4S/BBtkK/FxNFoKNkyPOAMnX6DS2guV42P8GdMe4e0YfWUX368BMt/DwgcCJ/d3wY9B3Nwby26ts52v0g5IHfFLnHy5yguEvGmhPBgEi9ct4D3Y6X8J6Ex0nZi/hakmiCnZHPRFnxMDeFyy84U4Qo//g3EGlVTeQuPiIH0h8Lwa1RbzhMCcwHdCiL6WED1tXBox4KAeEdDPiuhyVuvJgvca57g3iN3GtTVPCBHX1iaBDVAoJNFMKU8KHZOMEnRc/zsFThHPQlUhNjsnlBMbog0SsgaAPMgn8iXTzfAVHv+esyG2hZ68mK0eFXj1ruJJsiA6CREbhAX+NqSUrLfALmRwRUIctZdikMA7nnSbxPkjPyq8InBLDBaqCrHww4RjMQO2eHDQ2Nw+Dfcqiz3eZ03OWvNsp6ZCWdruouwV40nCMTBG95bk+LK4STRFSuuLncp197LQTciHLpMx7dik8/GtjLZsjj8F5sRJ9qmWKvsFi1sXX+nxl3s2JIh5EQ7WwXbxzfPw5komkflHaJLgh84maX35JV8P+fS7W/b4dxCqOt2tCTCXPcLFkcm0dzr0HBqe2xAhR28xTVqLMv7Pe440sE5I20Bf57tKZRK1lXKusFVgs9hA/ZLN11JIQ/bmPZzGuBLbDNDYSOy4+lsHxnmjZBYjvtSSyP+i6J5kGNVxBS0TrCNK3vuGQi56QAbYT89l6Ol5v/mjzjuCv2tph41UQ8hF42SA/cRchgH9LMkI+Oni1kDbaUWc9BcEEmfmARYLbQSf7lXF9Ft9RYAv8mzjnuuAW4moqQoSPeuMcqHA5kiisVJi+2qSUYKOnRrdfEMT7E01Qgz9TjVBHuWXzhf/00H/PPr0TUeqcjym7x2S1/eMR3l2azx5iOXmtvmUuhktyw85mew3Mf2EpUIrJ7xZ5ZuCn4U61aniEsfhXx5aLScCuVLo6BqgvxmOjys4vZCNtaSW7vdFmX2YzjTRiluyPPS2nD4TeGZ5Qp8VbNGZzxhhrAAdKSmKf6t5fIj11znNLRpqo4AMe69gO4ky6TqZ7WxHqjwd6irnEwL9/ZiiITYNtitS2FZ2k0INcL5gMd/sDZjYm7zIk4dY9GZ7l29Q3a/k4DdKP0QgUTN62phAad+sdQO6fETrZcwTBDUrKRJ/6zktm6aqU5EmwILxLEDthdrFXOm/lzRysrjC1/OVdIpCG4ATy6kL0QIJuSaNeoqpZZVI+bOrp/1qiLiXqtqXBNlsLrL+rP9c9pVdf0gDJBeCuL4bFHMFBf78SMpDa4kpcvRGu4yhDDk9JHkH3yjCv+7VeXsae3WfJWmBbEFKauX7PercSu3emKZIWiE/QCWS3L+V4SsgNMolTnhApeU4zI/bEWIdrizmyv5wmC1H2CJ+u29S0684QxIuS7oi6uIqO4hdyU48KJAXhMgWIO33e6gNk13lmDkmSChbOJ31n2BaRsWcLiwjzV8Qdyvm31KJhx2idZEGSFjttu4jfm1ET7WvJ5vh8cVsdAO0lvQ84U7hpWKLsj+cMAIFrRZILkL0gxPeoJKbxs8dQvZxst5S8LcB3kGy5Fx0kzMIBSOX77n+CgiNj83UzykmRQzYABOcjIWeHNFTvcWTTff4IHubpJYt3he0KPmuN5tBMTYmXu7a62GCSMnfEshyuVVmCx0En9j5LCT9jfIVMTybk422Uwg9bzFu51TMH3Q+FsYIlsD6A3pGFea/yBd6/Gvi0Z8UrvfksBw+5OjTHJ6CEc4YB7JovjkvEqDmAp0RYPTThFz0qAywjfta6Ob02IAjAoHoLNwjbBaQPyWkIXywj7u90rRxtm3IlWz+vM/DBJ6x7sIbArqvBLt1xZaiGqrNE7D7XugoQJ2ETQLyT4XobS9RWeIK2SZMEfiPnA3sD48/LH60QMe5qLEMSOBYyDj7qdLZprL+KJGRlMXdHlKVIW4TfNlYVYWe1ED9eRtPzJcKg4VqQhKxOWYKdtqLxNMO9fcFnvUgRRu+Q1ZbhQ3Oup1K3pC2wiGBTbFS2CekpckyfEwYLrwrhIh+SGbY+Uy8SNgi7BXSUh8ZLhJ4FwlaVSJuvKsFDswOYb3AbcAi5kNtZEzC3FLYLawRaOecUh31vkJgQWufwZEsVts/CQ3PYB9Z0+WMQKH8uDWmldM/l9tzMjgm5PNc5Goz01dwBAaoPd71CRXc7lC1x1U5soLbzZo7AxEYpjY5qWTrFUG91AhJ5viKaCxr4+xEgGSPT5yKIJInvnUzyiKQRSCLQBaBLAJZBLIIZBHIIpBFIG0E/gPU7xoOJMSO0wAAAABJRU5ErkJggg==\" width=\"64\" height=\"19\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, hence the output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 5;\r\ns_correct = 2030;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 55;\r\ns_correct = 17966;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 666;\r\ns_correct = 201462;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 7777;\r\ns_correct = 2342270;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 88888;\r\ns_correct = 26758054;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = double(intmax);\r\ns_correct = 646456993326;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = double(1e12);\r\ns_correct = 301029995664374;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nns = 10000:100000;\r\nss = arrayfun(@(n) S(n),ns);\r\nss = [sum(ss) ss(1:12345:end)]\r\nss_correct = [1490204856374 3011374 6727830 10443222 14159366 17876174 21592430 25308422 29024766];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-02T17:26:33.000Z","updated_at":"2026-02-07T14:04:07.000Z","published_at":"2021-10-02T19:50:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the integer triangle below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"158\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"167\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt follows the same rule as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pascal's_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePascal's Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e find \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is the sum of the n-th row.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Hence, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(1)=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(4)=14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe could be getting large numbers here, therefore please \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econcatenate the total number of digits with the last 3 digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and output a single concatenated integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(5) = 30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hence the output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2030\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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Sequences 78: Trailing Zeros of Factorial Numbers at any Base","description":"Given an integer  and a number base , write a function that calculates the number of trailing zeros of the factorial of  when written in base-.\r\nFor example, for  and , the function should return , because:\r\n  \u003e\u003e dec2base(factorial(15),4)\r\n  \u003e\u003e   '103001313131311200000'\r\nFor  and , the function should return .\r\n  \u003e\u003e dec2base(factorial(10),12)\r\n  \u003e\u003e   '1270000'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.45px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 12.6px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 188.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 94.1px; transform-origin: 407px 94.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 7px; transform-origin: 48.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5px 7px; transform-origin: 59.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a number base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224px 7px; transform-origin: 224px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, write a function that calculates the number of trailing zeros of the factorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 7px; transform-origin: 19px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when written in base-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 7px; transform-origin: 49px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 16px;\" width=\"33\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79px 7px; transform-origin: 79px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 7px; transform-origin: 30.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, because:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 36.8px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 18.4px; transform-origin: 404px 18.4px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 105px 7.5px; tab-size: 4; transform-origin: 105px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; dec2base(factorial(15),4)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 105px 7.5px; tab-size: 4; transform-origin: 105px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24.5px 7.5px; transform-origin: 24.5px 7.5px; \"\u003e  \u0026gt;\u0026gt;   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 80.5px 7.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 80.5px 7.5px; \"\u003e'103001313131311200000'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 7px; transform-origin: 11.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79px 7px; transform-origin: 79px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 36.8px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 18.4px; transform-origin: 404px 18.4px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108.5px 7.5px; tab-size: 4; transform-origin: 108.5px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; dec2base(factorial(10),12)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 7.5px; tab-size: 4; transform-origin: 56px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24.5px 7.5px; transform-origin: 24.5px 7.5px; \"\u003e  \u0026gt;\u0026gt;   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 31.5px 7.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 31.5px 7.5px; \"\u003e'1270000'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function z = trZerFac(n,b)\r\ny = x;\r\nend","test_suite":"%%\r\nn = [15 10]; b = [4 12];\r\nz_correct = [5 4];\r\nassert(isequal(arrayfun(@(i) trZerFac(n(i),b(i)),1:2),z_correct))\r\n%%\r\nn = 3:3:45; b = 2:2:30;\r\nz_correct = [1 2 4 3 3 8 3 5 6 7];\r\nassert(isequal(arrayfun(@(i) trZerFac(n(i),b(i)),1:10),z_correct))\r\n%%\r\nn = randi(13)+2; b = randi(34)+2;\r\nz_correct = find(flip(dec2base(factorial(n),b))-'0',1,'first') - 1;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 30:3:450; b = 20:2:300;\r\nz = arrayfun(@(i) trZerFac(n(i),b(i)),1:numel(n));\r\ns = floor([sum(log(z)) sum(z) median(z) std(z) sum(tand(z))]);\r\ns_correct = [346 2562 12 17 91];\r\nassert(isequal(s,s_correct))\r\n%%\r\nn = 100; b = 25;\r\nz_correct = 12;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 1234; b = 30;\r\nz_correct = 305;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345; b = 35;\r\nz_correct = 2054;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 123456; b = 40;\r\nz_correct = 30860;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 1234567; b = 123;\r\nz_correct = 30862;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345678; b = 1234;\r\nz_correct = 20041;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345678910; b = factorial(10);\r\nz_correct = 1543209860;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nfiletext = fileread('trZerFac.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java')...\r\n    || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'if') || contains(filetext, 'switch');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-11-06T10:21:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2022-10-26T10:06:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-25T12:04:07.000Z","updated_at":"2022-11-06T10:21:12.000Z","published_at":"2022-10-26T09:25:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a number base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that calculates the number of trailing zeros of the factorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e when written in base-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=4\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, because:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e dec2base(factorial(15),4)\\n  \u003e\u003e   '103001313131311200000']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e dec2base(factorial(10),12)\\n  \u003e\u003e   '1270000']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57417,"title":"Easy Sequences 86: The \"real\" Hyperprimorials","description":"In Easy Sequences 85, we define the hyperprimorial of , as a exponent ladder of primes numbers from the -th prime down to first prime (). OEIS, however, defines hyperprimorial differently. In OEIS sequence #A076265, the hyperprimorial of , ()  defined as follows:\r\n                             \r\n                             where:  is the -th prime number.\r\nUsing the above formula, we want to calculate , which is the sum of all hyperprimorials from 1 to n:\r\n                            \r\nFor example:\r\n                            \r\n                                \r\n                                .\r\nSince this will involve large integers, please output a vector containing first 6, last 6, and the number of digits of . Therefore, the final function output should be:  .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 430px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 215px; transform-origin: 407px 215px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.5px 8px; transform-origin: 7.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57412-easy-sequences-85-hyperprimorials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eEasy Sequences 85\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define the hyperprimorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as a exponent ladder of primes numbers from the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime down to first prime (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 221.5px 8px; transform-origin: 221.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). OEIS, however, defines hyperprimorial differently. In OEIS sequence \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A076265\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#A076265,\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5px 8px; transform-origin: 13.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe hyperprimorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 76px; height: 45px;\" width=\"76\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                             where: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.5px 8px; transform-origin: 55.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 163px 8px; transform-origin: 163px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eUsing the above formula, we want to calculate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, which is the sum of all hyperprimorials from 1 to n:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 74px; height: 45px;\" width=\"74\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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936/fwTzXJSNGs/qvhGHvDm5wjBWTNV4ntJl9CSE3YFhLJa3OyhZr+1eWrL0DiEKSznQ5j42Q1rqkqXexBS561cIt8Sdrlee6lK6SRYvtN+a6Xc4UTTlZZf9Ln0GInfh2LkOvKkvv+7cvRQAILjkGCGMTP1lADFLDxCmJPcTUPCDrZBQN6e1sKnQFUdLHl4NHwPIpg5OmYITDRdrdq3XjJemsxch7E5AUzy6XFvHfl57yVJPEzK52++15C59FBtbfpeSW+pGbnKXgvbuHnIXjp2L1ZRDTufukAPCgkuOFcLI2N2ENRWNYOwo4hJrO4MfrHJC97jp1MGmVJXdg1CQ51J97pI0uj54jiP/iwDybmVjYCx2vQhhd2CY4tH9VDTmMY7FZi790pKlC+RmiHG8UGFzw9SVumSppwmZ3PUrhFvjDmPvmZn+pJtmMR4jdvzUhSPUU5wW7Hfpoyi5C8dOnTpTDjm3HRbVk2NCGMIIn1cen6i/L7R897QeQ/xZ7/4fzOTpF7X0CTYU2tRPsKH5azolsIVjiWM9vO765jkPP57xJ2II16UXQpnEHKTCqBFxLUu5mXr7dbleigwSV3Jaaq4RPsaN3PUrhHvjjmuE++135G7Hnasrp4INuE67ossAx4QwBoE7xOaWMbifY30hjMnwEjF/U0/M1Lr2J9iYuqr3uwUhgnqHeniR1j90Y8rrCD4eFAs9tncKP0aNCG9Z7sAwtSzC/TpTbL1UeBVPpKQQPjmok7sdJr14FXvsdxRT/fY7crfjznXqTC2L0HX7IeciRE1jY0IYYmVp7a8b4gKfQ90LlcVnUQin1MDHS59gQx8y9RNsaP66LriFcGla51APL9K7yx3m1txAcL1a7BNiqYc3oDxGjQhtWcsDg7uxYKm/hpeal5JCOGxQJ3c7nJb2Lyy1Rovd60sTcovcUUz12+/I3Y4714E3pkvdA8KWlnsujRsn/u4XqB5C7Pq+Tmxsh6n7xux7QcfWkUIkfmQir+gKN3SDPuvaESJcSHwP79LmKXct95SY9/NEedbh86xp7mGN8NzA4K5JL7pWKhN4CuHlQZ3cHTeyFoVwj/2OYqrffkfudtypA28syhVePr8nhsOjTJw+vhAO2ems4mlso5Su7f0nqfAZMT0JpLgrO3PCzr1diYH3O3e5QG5d3PtDPbx6j3voxtz6ZrSL54u9WQzhsfRq4XN8Cn49CGFsesGLzFjf0T64JIJ1kC3+Bj0BOoXwDhhyd7KB9LI0okfuKKb67Xfkbn+Jpu9cdR0HSyI4eb7zhbBOZBC5mIShzrG84M9irrgNjRaAwe/rYmZKPkUFZd7jBma+XPLKPe43szr/uF03KYI3XEsc+ZE9Qjf64fkhwLBUYkmIlXq20vm0LoRdL7z7xQG/B2/YJX692FI4QgwMSJtyHGUK5hTC+4M6uTtuRT0I4V77HcVUv/2O3O0v0XS/TOveJESRuDFAayXPd74QxjoMHMWLiBEYFDCJ4vxn/IwLUQPmIkqMTZ665irkYIeUybfmPe7bSUsHT8AT/G9iL/DA+JP8/2tibmQHpHU5dW8J5dc9QCQlBF9NzsbKal0Iu559DAwYCPT6vvywJIDXwpdC+OSgTu52rbEHIdxrv6OY6rffkbudc0e/NGO51LlicJ4+IwbdaO5srCVi8LkJE8Kla83QhcrVRhvqPS1UbJPZaOPtcXlE60LYjQZRq4+WaGQQO5eJxYbVCy27BzFF7sbZJHehrTw+HQT8KbGYEKUxpZC7GLTi0pK7oyNdormas7TWJAsBCW9qz0J4zTBpwO6dYvfF9THT1Or9oxAePz0o54tB7sCgg+sV0gIeFvuMaUuol3kPEzK561cIkztyxzFzeTwvGa3FjcKSunk2e76rJYSxI/BRsbPLGDeZQj+ZrbUmFjuZfy4Wc3iFNZCo0+lOX25a9giXGBjAvQ5WRQOPWzeqhfxbF8LkbppAcrdy58kontxlgLfyra1z54ZFy3EeZc13NYSwbkCotXO9dLvTNc5rhUlD+f8tZn18bixuWO6CuMI9ehtbFsIh562HcAXvFi5sakw5VjWkjNppWh/UyV2/QpjckTuOmWEjekmPsJtXjh7N4i6nYB8y1xuiXijdXPa5TgWThknDs14oNhZXOazppKWCJxpLMuAJxjnxa1z6udANa4I64eo1PnSrQtjdhAh8U9+QtS+utubKqKG2LITJ3Tzp5M6oU1TIltxVANmoiJa5cw+vQZQrfGFOcdpkz3clhTBE70fFIN6w4w8eVCyJeESs1V3uc20Pz/P0kKB2mDSU/T6x24by1/Smw1NykxjCsmHDI0T5/4n9r1jtF4NSY0WLQlg3mo09Y+zacP3clLrmqhTOpfNpdVAnd8tMk7tljFpNQe5aZWa5Xq1yp+t6/SdI2WidPd+VFMLLlPSTwg2TVnONJbxK2BSHUCJ4mcA1d/RxP4i2VdMWhXBJhJIDi5eshEFerQ7qJR+V3IWjWfITbXip0ynJXTiK5C4cq5yUHDMD0KMQHgdJQyBZhkmD6D1P7GIxuPbxWUAPw3BrtXSaSgDNTOIgMDYw4M9Lx1HPgTg2qE8dWV2DDAh9PVAFJx/2+EVmDCd3Haf+PedFUb/66Eun5mnZ75f4J3dLCO3+Tu7CcCqRiv2uBIrr5EHuAnCnED4JkhvcGWssS10XTAjdpfxzBNpS3of0d0ycV4qBX1/4AAcIqtvFYpZ84AXmVrFrJ4CEGMZmQvOA4E75KvRRNq5elya5kOKl8S1i907grCdgxgh+rE+7UwybCf0LS4DuEXtILGXNWmq/IndhyJG7MJxyU7Hf5SK43v3kLgJ7CuF9sNyThSJgNEu6Vrg2swdaIeMxb21INabW1055lEPyTN38FpK3pnGPAIdI7zGqhz6Lv4QlFIcpnMe8I6F51hgryd30BlFyF9pS89Ox3+VjuFYO5C4B+RqDe0K1VrsFoqml636pTIyXq6W6t1IXxDt+VUJlHpR7xuI2wws85ZlcKgbiuqZ3eKk+rf89tT9O4YwX3TOJD31V4n2Hehu565d5ckfuFIGDGDMphPtt8Kw5ESACRIAIEAEiQASIQAYCFMIZ4PFWIkAEiAARIAJEgAgQgX4RoBDulzvWnAgQASJABIgAESACRCADAQrhDPAK3KqHkFwqecF49YuArh3+iTzC2X4f4yBrTu76pZ3c9csdon9gH8x7xbgXpi8eN8UdhXBc49OIAbnRHCCAEQ7qRjGEb8IpfBTCcVzkptZd6LlxmjVMzYelQgjL5h5FnVtH3j+OALnrt2WUOnSC/a5+GyjFHebRq8X05NSah1bVR62NEsndDA8UwnGNtKQQPleKxoEaj1EIx5FQKHVJMfWc1AknAiKaBIVwIYJmsiF39hhblYAJ+TVi14g9nlEIhDD7XQaACbeW4g5efETPUXFGIZxARuQt5I5COLLJ1Euuwpoe4XqYW5Wk4oxC2Aphu3zJnR221jmTO2uE7fKnELbD1jrnTXFHj7B1c5nPn0J4XfxLls4JuSSadfMid3XxLlkauSuJZt28NiWm6kK3emmb4o5COKw96Xq08yU5fr5O7A9ht86mohAuAGJkFsD8MrFLxJ4Ve0/k/VPJOSEXAnImG3Jnj7FVCQjMf0rsCrGHxUqdeMh+Z8XYcb5W3G1KTNnTkFQCuQuAjUI4AKQhiS9aY4/aHVv+QCEcjn/JlP7kGXt869jyB07IJRmazovc1cHZohRf+LDfWaBsk6cFdxTCNlz5ufo46/9DSx9bw70p7iiEQ5vC0dHNkvQBMRVBiPxwUfjtf0/pbw6hEI4EsFByHJ18rZh2cHj5sXEx9PqLJPSPSqYQDkUvLx25y8NvzbvxBQYXIuX8Roz9bk024sq24G5TYioOzqqpfe6wWfGciBr8buiv7i2b4o5COLw16AT8uhFBG57LfkoK4VTk8u7DwAA7PdLBU3OmEE5FLu4+cheHVyupMfk+JfYdsasKVor9riCYE1lZcbcpMWVPQ1IJ5C4ANgrhAJCGJBYTMIVwOP6lUloNDJyQSzE0nQ+5s8fYqgT9ovYhKeC+goWw3xUEcyIrK+4ohMmdPQIBJVAIB4AkScbiB3ONcBh2raUai0HLtYqtsTReH3LXB09jtRwL6M9+1wefVtxRCNvzP8Yd1wh7uFMIhzVEdwL+hdzyy+E2rhEOw6+lVO7A8FKpGI725FrFlhiargu564OnsVr+VX75a7HXDsZ+1w+XVtxRCNu3gTHuuEaYQjip5bkd9gbJ4RaxEuHTcF73N8R4oEYSLUk36cBwu9z9CrGzSbmcvOku+RWODOWBGoUAHcmG3Nlha5mzfj379FDII8MLaIky2e9KoDidhyV3T0qx2DjJk+VsOCR3gbjSIxwGlA62X5bkd4v5EQPCcjlOhYgTV4q9fxgI8BesncNGkty8Y+tyaOl18IVg/aRY7gsNvMngEu3ihWJ/FENs4h+JYWc8r3IIkLtyWNbMCX0EL/u4bhUrEUOY/a4OgxbcwSP5VjE4DnChbdwh9kSB8bgOKn2UQu4CeaIQDgSKyYgAESACRIAIEAEiQAS2hQCF8Lb45NMQASJABIgAESACRIAIBCJAIRwIFJMRASJABIgAESACRIAIbAsBCuFt8cmnIQJEgAgQASJABIgAEQhEgEI4ECgmIwJEgAgQASJABIgAEdgWAhTC2+KTT0MEiAARIAJEgAgQASIQiACFcCBQTEYEiAARIAJEgAgQASKwLQT+BvVKiPFVUPRQAAAAAElFTkSuQmCC\" 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style=\"width: 441.5px; height: 19.5px;\" width=\"441.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 190px; height: 18px;\" width=\"190\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115px 8px; transform-origin: 115px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince this will involve large integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264px 8px; transform-origin: 264px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eplease output a vector containing first 6, last 6, and the number of digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.5px 8px; transform-origin: 152.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, the final function output should be:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 163.5px; height: 20px;\" width=\"163.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    s = sum(hyp(n),1e6);\r\nend","test_suite":"%%\r\nn = 5;\r\ns_correct = [793011 987612 23];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 10;\r\ns_correct = [210753 400112 157];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 25;\r\ns_correct = [331784 287612 1846];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 50;\r\ns_correct = [493074 400112 10866];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = [616091 125112 60156] ;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 111;\r\ns_correct = [135700 562612 77760];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 222;\r\ns_correct = [502853 800112 407761];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 333;\r\ns_correct = [118917 137612 1060631];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 444;\r\ns_correct = [571761 200112 2075648];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\ns1 = []; s2 = [0 0 0];\r\nfor n = 401:450\r\n    s = S(n);\r\n    s1 = [s1 sum(s)];\r\n    s2 = s2 + s;\r\nend\r\ns1_correct = [3399227 2462755 2513309 2591563 2945479 2629800 2429946 2004548 2424123 ... \r\n              2821874 2678061 3274455 2940458 2534820 2560707 3108793 2977734 2787069 ... \r\n              2663207 2472829 2131208 2833671 3029902 3318271 2420784 2658659 3118743 ...\r\n              3225127 2317337 2461778 2482161 2841696 2309811 3155290 3027882 3307035 ...\r\n              2592649 2263026 3857175 3256909 3238654 2485976 3765395 2847521 2904752 ...\r\n              2475937 3468958 3034826 2828495 3129026];\r\ns2_correct = [22037407 24793100 94178904];\r\nassert(isequal(s1,s1_correct))\r\nassert(isequal(s2,s2_correct))\r\nassert(isequal(sum(s1),sum(s2_correct)))\r\nassert(isequal(sum(s2),sum(s1_correct)))\r\n%%\r\nn = 500;\r\ns_correct = [221421 175112 2738917];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 555;\r\ns_correct = [146871 37612 3486572];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = [315383 850112 13508037];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assign') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-12-14T11:15:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2022-12-14T11:15:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-12T11:08:08.000Z","updated_at":"2022-12-14T11:15:42.000Z","published_at":"2022-12-13T10:19:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57412-easy-sequences-85-hyperprimorials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eEasy Sequences 85\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, we define the hyperprimorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, as a exponent ladder of primes numbers from the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime down to first prime (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). OEIS, however, defines hyperprimorial differently. In OEIS sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A076265\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#A076265,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe hyperprimorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n=\\\\prod_{i=1}^n p_i^{p_{i}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                             where: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUsing the above formula, we want to calculate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is the sum of all hyperprimorials from 1 to n:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n = \\\\sum_{i=1}^{n} H_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_5 = \\\\sum_{i=1}^{5} H_5=\\\\prod_{i=1}^1 p_i^{p_{i}}+\\\\prod_{i=1}^2 p_i^{p_{i}}+\\\\prod_{i=1}^3 p_i^{p_{i}}+\\\\prod_{i=1}^4 p_i^{p_{i}}+\\\\prod_{i=1}^5 p_i^{p_{i}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e=2^2+(2^2\\\\cdot3^3)+(2^2\\\\cdot3^3\\\\cdot5^5)+(2^2\\\\cdot3^3\\\\cdot5^5\\\\cdot7^7)+(2^2\\\\cdot3^3\\\\cdot5^5\\\\cdot7^7\\\\cdot11^{11})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e=79301169838401181987612\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince this will involve large integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplease output a vector containing first 6, last 6, and the number of digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, the final function output should be:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n=[793011 \\\\ 987612 \\\\ 23] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57512,"title":"Easy Sequences 89: Double Summation of a Trigonometric Product","description":"Given and angle  in radians and a positive integer , evaluate the following product summation:\r\n                    \r\nwhich 'directly' translates to Matlab as:\r\n    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nFor example  and :\r\n    \u003e\u003e x = 3; A = 1;\r\n    \u003e\u003e PS(A,x)\r\n    ans =\r\n        8.9683\r\nPlease present your answer rounded-off to nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 492.078125px 144px; transform-origin: 492.078125px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven and angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e in radians and a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the following product summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"236\" height=\"46\" style=\"width: 236px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich 'directly' translates to Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 40px; transform-origin: 489.078125px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; x = 3; A = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS(A,x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        8.9683\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = PS(A,x)\r\n    p = sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nend","test_suite":"%%\r\nA = 1; x = 3;\r\np_correct = 8.9683;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2:2:20; x = 3:3:30;\r\np_correct = [1.8697 -3.3674 -62.4997 11.5088 -4.8523 -71.5196 25.1022 -3.2420 -64.7730 49.3233];\r\nassert(isequal(arrayfun(@(i) PS(A(i),x(i)),1:10),p_correct))\r\n%%\r\np_correct = 4166.0746;\r\nassert(isequal(sum(arrayfun(@(i) PS(i,i),1:100)),p_correct))\r\n%%\r\nA = 100; x = 200;\r\np_correct = -739.8950;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2000; x = 3000;\r\np_correct = 2041.1906;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 10000; x = 20000;\r\np_correct = -3131.6478;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 200000; x = 300000;\r\np_correct = -8386548.7261;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 1000000; x = 2000000;\r\np_correct = -11067350.2876;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 123456; xs = 200001:200100;\r\nps = arrayfun(@(x) PS(A,x),xs);\r\nss_correct = [-88558 -88558 -88580 12]; \r\nassert(isequal(floor([mean(ps) median(ps) mode(ps) std(ps)]),ss_correct))\r\n%%\r\nfiletext = fileread('PS.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T06:37:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-06T09:42:25.000Z","updated_at":"2025-11-22T20:00:54.000Z","published_at":"2023-01-07T06:37:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven and angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in radians and a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the following product summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ePS(A,x) = \\\\sum_{n=1}^{x} \\\\sum_{m=1}^{n} \\\\prod_{k=0}^{m-1} 2 \\\\sin \\\\left( \\\\frac_{k\\\\pi}^{m} +A \\\\right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich 'directly' translates to Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e x = 3; A = 1;\\n    \u003e\u003e PS(A,x)\\n    ans =\\n        8.9683]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57954,"title":"Easy Sequences 108: Enclosing a Circle with Primitive Pythagorean Triangles","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and . \r\nWe say that pythagorean triangle is a primitive pythagorean triangle (PPT), if all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are a, b and c, it is PPT if and only if: gcd(a,b) == 1 \u0026\u0026 gcd(a,c) == 1 \u0026\u0026 gcd(b,c) == 1.\r\nGiven a circle of radius R, find the dimensions of the PPT with the smallest area, that can enclose the circle, without touching the circle (i.e. no sides is a tangent of the circle, or crosses the circle). For example, in the figure below, if R = 12, the smallest pythagorean triangle that can enclose the circle without touching it is [39,52,65]. However this is not primitive since, gcd(39,52) = 13 ≠ 1. The correct smallest PPT is the triangle with dimensions: [48 55 73].\r\n                                                   \r\n-----------------------\r\nNOTE:   There can be more than one PPT with smallest area for the same value of R. For example if R = 4.5, there are two possible smallest area PPT: [20 21 29] and [12 35 37]. Both have an area of 210. In cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter. So, for R = 4.5, the function output should be: [20 21 29].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 547px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 273.5px; transform-origin: 407px 273.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePythagorean Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a right triangle all sides of which are represented by integers. Examples are triangles with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGQAAAAmCAYAAAAycj4zAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAZKADAAQAAAABAAAAJgAAAAANiNVoAAAE9ElEQVRoBe2YfYgXRRjHr1fpxCsxxZc6NV+TREpRIjvhKuKMIMsKxCSow0JICat/igzFSML8QzI4/5Go6Ao1CklBKZUsSwvier87KnxLlEOtLkzr87WdY357u7O/2935XcftA5/fzD4z8zzze56dmd2tqiqkiEARgSICRQSKCKSLwEUxw25C/1ZM25voX4hpK9SlEWjisq5U1XVVT+1Q11VQuTSsCK6voJwIX8DRQGeKDlMpysQItNBjeKjXaK6ngmLcTeJWyC303AvzYGu3UdGK2ahnwiRQ5vfBp3AaKiVX42gNtMEqT05HYndUhG3FchbMhYaIdqNaTOU1mAA/GWVSqYT8A/ckdaRdk/sA1D+MEnMDVEp082gOn3h0qBst/D/t6yUJvpUQ9R+f0K+kudyEVDPqS5CDA/BOUNoTPInuKvAtjTgwfn0l5FbLh/Fll6doH5TwR50JiTtDEmx2Na+mNhkehOYubVXVWOpaNVNgMOgA2wy+RMv/FV/GLbtPU/8b1sA5S2+q26h42aLLWSE1gXOdM1FyP0pz97wc1SEnnW6qz6AdOkE+fawQ3Vzn4XXIIs4VcnEGy9cxdh1sibFxzNL/bNXzrj6PwRmwCLRl+JLlGNbB/V5Q+vITabecFRI50FI+S113q5b29ZY+z6rmqS3kxcDob5Q+VoierP4KbMv+CXgfHoKB0BNxrpA4Q1kTchmGD4ImvwJ8iA5PPd7Kj/xJfCXkJWzrv0RxEv0CKFecCcmyZcVNoJoGLesbYUUARe6yHosjYCGczd16qUElej+cKVVfuBrM7xvwXERbbqo0K0TJbQCzMnQ3aU9/AvIW88AQtu1rhZj56wypBZ1X7RBeMfeiSxLnCokb3NOEaFW0QniC5nppnKMU+msYo21iByhAtvhOiO1rABd6DLbPlu+4Ttp1KpIQTVTbhw7vu2EnmGSo7IChkFWUANnWoaqDNiyVTIjx/TgV+7/ONg0xpTMhSdmMsRmpPoL2W9DTx+2giZo990rqd0BWeRID9fAYHM5qLKfxG7DTbNkabdV7XNVLlQ/RHaMPaGPgGZDojT6LaLy+DHwPOpvuhLDoyUuiTzWm/Q/qe6T0KO9i+4HA/rAsfnwlxMzpQyomIXoaySJKyOUwCWTXJdo6TR89Go9zdc6hTQ8yRrQ9pxbfCdEnjPOgrfHH1LP8b6BWnWy5xN6CTd9zrgE5tXVadrR1pxb7D6Q24hiorcP4+NrRr5wmvdtcksDxwNA+q9/EQOezmBYY1+r4OIsjE6wsNlxj7woav6L8yNWxj7fpYUOyCf68UEv5kyUhQ/C5EfT1c1aEfz3mrgRtGU+Btpy+KPos0g4tsATCMWtEdxvoYWM1eJFyXgwfwbOCbPZ2fT7Q0tX7wXz4BbS33geVEh/vIZuZvPmfKrUd1sF0WAvS/QBR70Wou8liNBozvluLQ1FOQmoY/yvYk1Vdh2krvAp6q66k6CbQHHbl6HQmtg4FdsP/VfplUA3lijMhWZ6y9C4wAebAKNDW9E3A75S9IbUenO7H5hi4Ga4FBV83Yju0wVnITbIkRJPQlrQ9t9n8fw0p6LsrMb3wAVUJn4UPRwSKhDiC0xtNSVvWw0wq/PXyc3Rv98Zk+6DPR5lz+BteXZr/MYNB4ScKc92UxmA/HbPFEcex/TQmxd8uIlBEoIhAEYEiAv0jAv8CgUAwjj+ULvgAAAAASUVORK5CYII=\" width=\"50\" height=\"19\" style=\"width: 50px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"19\" style=\"width: 65px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe say that pythagorean triangle is a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eprimitive pythagorean triangle (PPT), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, it is PPT if and only if: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a circle of radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the dimensions of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, in the figure below, if\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e R = 12\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[39,52,65]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. However this is not primitive since, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(39,52) = 13 ≠ 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[48 55 73]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104px; text-align: left; transform-origin: 384px 104px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                   \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"354\" height=\"202\" style=\"vertical-align: baseline;width: 354px;height: 202px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-----------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e There can be more than one PPT with smallest area for the same value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, there are two possible smallest area PPT: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[12 35 37]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Both have an area of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e210\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e So, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the function output should be: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ts = minPPTs(R)\r\n  y = x;\r\nend","test_suite":"%%\r\nR = [4.5, 12];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[20 21 29] [48 55 73]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = 50;\r\nTs_correct = [160 231 281];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 100;\r\nTs_correct = [336 377 505];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 200:50:800;\r\nPs = arrayfun(@(r) sum(minPPTs(r)),R)\r\nPs_correct = [2378 3008 3570 4240 4902 5368 6030 6432 7100 7592 8374 8848 9396];\r\nassert(isequal(Ps,Ps_correct))\r\n%%\r\nR = 900;\r\nTs_correct = [3045 3172 4397];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 1000;\r\nTs_correct = [3255 3712 4937];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = [123 1234 12345 123456];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[429 460 629] [4176 4343 6025] [42036 42427 59725] [417543 425776 596345]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = randi([100000,1000000])\r\nTs = minPPTs(R);\r\nr = prod(Ts(1:2)) / sum(Ts)\r\nassert(gcd(Ts(1),Ts(2))==1)\r\nassert(isequal(sqrt(sum(Ts(1:2).^2)),Ts(3)))\r\nassert((r\u003eR) \u0026\u0026 ((r-R)/R\u003c0.0005))\r\n%%\r\nR = 1000000;\r\nTs_correct = [3404505 3424952 4829177];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nfiletext = fileread('minPPTs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-12T18:05:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T11:52:42.000Z","updated_at":"2023-04-12T18:05:02.000Z","published_at":"2023-04-12T18:05:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePythagorean Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a right triangle all sides of which are represented by integers. Examples are triangles with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3\\\\ 4\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe say that pythagorean triangle is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprimitive pythagorean triangle (PPT), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, it is PPT if and only if: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a circle of radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the dimensions of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the figure below, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e R = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[39,52,65]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However this is not primitive since, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(39,52) = 13 ≠ 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[48 55 73]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"202\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"354\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-----------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There can be more than one PPT with smallest area for the same value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there are two possible smallest area PPT: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[12 35 37]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Both have an area of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e So, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function output should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMwMgAAkpIAAgAAAAMwMgAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Sequences 91: Generalized McCarthy-91 Recursive Function","description":"The McCarthy 91 function is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\r\nThe McCarthy 91 function is defined for integer  as: \r\n                                        \r\nRemarkably, the function yields  for all  (hence, the function name).\r\nA more generalized form of the McCarthy's recursive function is defined below: \r\n                                        \r\nFor positive integers , , , , and . \r\nThe expression , means applying the function ,  number of times:\r\n                                        \r\nThis means that the 'original' McCarthy-91 function  is actually , with , ,  and .\r\nGiven integers, , , , , and , evaluate the value of .\r\n--------------------\r\nNOTE: The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 454px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 227px; transform-origin: 407px 227px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/McCarthy_91_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMcCarthy 91 function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 286.5px 8px; transform-origin: 286.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167.5px 8px; transform-origin: 167.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe McCarthy 91 function is defined for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e as:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 366.5px; height: 18.5px;\" width=\"366.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemarkably, the function yields \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 70.5px; height: 18.5px;\" width=\"70.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 51.5px; height: 18px;\" width=\"51.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89px 8px; transform-origin: 89px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (hence, the function name).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 280px 8px; transform-origin: 280px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA more generalized form of the McCarthy's recursive function is defined below: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 291px; height: 19.5px;\" width=\"291\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5px 8px; transform-origin: 66.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe expression \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 61px; height: 19.5px;\" width=\"61\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, means applying the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eG\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number of times:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 52px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 26px; text-align: left; transform-origin: 384px 26px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 165px; height: 52px;\" width=\"165\" height=\"52\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis means that the 'original' McCarthy-91 function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 37px; height: 18.5px;\" width=\"37\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is actually \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 51.5px; height: 18px;\" width=\"51.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 43.5px; height: 18px;\" width=\"43.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36px; height: 18px;\" width=\"36\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = M(a,b,c,k,n)\r\n    m = G(n);\r\n    function g = G(x)\r\n        if x \u003e a\r\n            g = x - b;\r\n        else\r\n            g = G(G(G(G(x+c)))); % k-times\r\n        end\r\n    end\r\nend","test_suite":"%%\r\na = 100; b = 10; c = 11; k = 2; n = [1:20 201:220];\r\nm_correct = [repelem(91,20) 191:210];\r\nassert(isequal(arrayfun(@(i) M(a,b,c,k,i),n),m_correct))\r\n%%\r\na = 333; b = 3; c = 33; k = 3; n = 33;\r\nm_correct = 354;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 4444; b = 444; c = 444; k = 4; n = 444444;\r\nm_correct = 444000;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 55555; b = 555; c = 5555; k = 5; n = 5;\r\nm_correct = 56145;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 7777777; b = 77777; c = 777777; k = 7; n = 777;\r\nm_correct = 7700875;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 999999999; b = 9999; c = 999999; k = 99; n = 999;\r\nm_correct = 999997623;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 9999999999; b = 9; c = 99999999; k = 99999; n = 9999;\r\nm_correct = 10009111707;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 7654321; b = 891011; c = 171615141312; k = 181920; n = 1:100;\r\ns_correct = 952242024250;\r\nassert(isequal(sum(arrayfun(@(i) M(a,b,c,k,i),n)),s_correct))\r\n%%\r\na = 10000000000; b = 1000000; c = 1000000000000; k = 1000000; n = 1:1000;\r\nm = arrayfun(@(i) M(a,b,c,k,i),n);\r\ns_correct = [9999000500 9999000500 9999000001 288];\r\nassert(isequal(floor([mean(m) median(m) mode(m) std(m)]),s_correct))\r\n%%\r\nfiletext = fileread('M.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-19T04:00:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-17T23:39:34.000Z","updated_at":"2025-08-23T09:20:38.000Z","published_at":"2023-01-18T08:07:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/McCarthy_91_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMcCarthy 91 function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe McCarthy 91 function is defined for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e as:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n) = n-10 \\\\ \\\\text{if} \\\\ n \u0026gt; 100 \\\\ \\\\text{and} \\\\ \\nM(M(n+11))  \\\\ \\\\text{if} \\\\ n \\\\le 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarkably, the function yields \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n) = 91\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\le 101\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (hence, the function name).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA more generalized form of the McCarthy's recursive function is defined below: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n) = n-b \\\\ \\\\text{if} \\\\ n \u0026gt; a \\\\ \\\\text{and} \\\\ \\nG^k(n+c)  \\\\ \\\\text{if} \\\\ n \\\\le a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe expression \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG^k(n+c) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, means applying the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e number of times:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG^k(x) = \\\\underbrace{G(G(G(...G(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{k times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis means that the 'original' McCarthy-91 function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is actually \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec=11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57565,"title":"Easy Sequences 92: Number of Roots of a System of Linear Diophantine Equations","description":"One of the tasks that Matlab is very good at, is in solving systems of linear equations. \r\nIn this problem we shall tackle a system of linear Diophantine Equations in which the roots are limited to certain range.\r\nGiven the number of variables , positive integers, ,  and a root limit, , create the function, numRoots(n,a,b,L), that outputs the number of posible integer root sets of the following system of equations:\r\n                \r\n                \r\n        with:\r\n                .\r\nFor example, if , the system of equations:  and , where , has only one root set, namely: . Therefore, numRoots(2,10,4,1) = 1.\r\nIf , two of the possible roots of:\r\n                ; and\r\n                \r\n                where:  \r\nare and . In fact, there are  possible root sets. Therefore, numRoots(4,20,6,3) = 16.\r\nThere are no possible roots for  and , therefore in these cases the function should return: numRoots = 0.\r\n-------------------------\r\nNOTE: As an added challenge, only those solutions with Cody program size of less than or equal to 200 will be accepted.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 607.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 303.75px; transform-origin: 407px 303.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 270px 8px; transform-origin: 270px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the tasks that Matlab is very good at, is in solving systems of linear equations. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem we shall tackle a system of linear \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Diophantine_equation\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDiophantine Equations\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145.5px 8px; transform-origin: 145.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in which the roots are limited to certain range.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the number of variables \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epositive integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a root limit, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 68px 8.5px; transform-origin: 68px 8.5px; \"\u003enumRoots(n,a,b,L)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 281px 8px; transform-origin: 281px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that outputs the number of posible integer root sets of the following system of equations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 249.5px; height: 20px;\" width=\"249.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"width: 378.5px; height: 21px;\" width=\"378.5\" height=\"21\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e        with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 132.5px; height: 20px;\" width=\"132.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83px 8px; transform-origin: 83px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the system of equations: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJoAAAAoCAYAAAAG/eNpAAAFtElEQVR4Xu2bScsdRRSGkx/gFF25EHFYiAuFOIDoRnBAQQgRNAoSUNAouHMWXDhnIwSiiWtDdCtxiC4EJ3CCCIILB0TElSP+AH0f7SPnq1vVXXVvd3/d362Gd3G7azqn3jp1zqm627fVp2pgBA1sH6GP2kXVwLZKtEqCUTRQiTaKmmsnlWiVA6NooBJtFDXXTirRKgfQwEXCl4WqoM5Jwl85dSvRCrW7xYpfKXkeFy4TdmTIdrrK3Ck8LLwk/ClcLZwn3C+8mWqjEi1Du1uwCNboeeG6RrbfM4gGyd4WLhFuDEj1qn7fIjwjPBbTVyXaFmRRh0h36/spwlfCK8JpQg7RjEyvqfytQR+Q8JumrZCE/xadE9FYTazAe4TD68ePQSQ2nXYRjS32g2YEUSLp24vCPuE74XLhVz/iSrRB5m82jeYSzawZhGTr/D4iIVbuaIqMlWiz4cQgA80hGtviL03vWCsc/9iD33ei+UCgcG+pRcNsxkLYc/T+TOHr0EwOopL/HNGhtk4L1T8Mxo6SLxB+TqzigUQdrdkcovltM+af+cH+nSJkyqLhMO5qJpa6ocl8Wu8ebRpNRho9q6tvot2g8d0hXCvgEPN4/4OtAL+Db8eF23tcUEbsVVUULozS9nKIBhcONQ3nEo3iZ3h9pYhmCTy/75oTDsmYnM8EnL+xnPO+iWYyYpnZEnhMkZCQiIwtABnfEcJIq3RSfXmTZZU2uhz4nLZziPagGiIV4vWTatssGt8vFv5PAuf4aFYZpR8TDgipfTpHuGXL9E202MR/rpd3Ce8JKad32fH7eizWnSs29EcP5C8lWpdR8QuomGhWmVVP9vh8YUPouqLCrLr5fKnmXmgmn636rZY+l/EZ/aqFbE8IySx3T/JOoZlSoj2kQe9vGTi7HAuUp5hofhK6GL2K8nw/q7SzQcDMhkoc3swmZ1GslGglPlox0XKSdV6rdrzxhV5GjyMSU4APtLdlejiPwzHHsn7bUo6wOpbn6Zp5cxHaghui0CcFfNRzBfyk5zpWeVe/m/k9h2gli9B0uOA/5vhoPj/SZjrZ+m4WOHCFEH1Ho0P6aBDok4Y8RJjXR2bfzvoIDNi6LxSebWRN1UmRaE5RZyxYSsllRMP9uNQX6iKanwDqLTTgGmNAnOZzuk+UMieiWebbxNkQmjcvCfPPEryV9ouwZMueU9SJ+OwgZsFTtzy85VuY+y6iMQG/CT805KHT2CR48pqvNReiQaAHhL1C23keuiB3GG7L5gCnzgBjq39OUSfj9/4zhIu5Jj7ftrDo2ohGRUJ9TGDMT+PdFUIYhcyJaGaRbPGEfhoW/aDQlkMz61Ri0WLk24x3OT4a4/K3M1Luky24aMDgiYbSOeLh+sjJAllxn8rw+TRuT5BriqU6pkw0u7j3o8b+k/C6cJNgGXZTPC4C96tQWleqwwKThRsLm8Gcwj5ziUazJLHfEGK3M8wQ8Y1AacHieaKFfkO4QkM/JrWCp0y0MIUSpmu8+Ue5Xekcc5T3qCz6mdPjdynGfZVbcCk57KSI4Meie9phweJi7RaiV8I90WAs13HJOBNNhRWweI80I4h9t8FNmWgmw6kaLCccYVLW0hcQKPY9nACsPs7xfcIQSewhiAsxbhOQMXxISX0U0YsvZ9kFrnDzYL3eF95t00FXMLCMoEMRjdVE1PexsOph8jJyhXWYME4r2GKXydv1MYbZtDEnok1Jqaxq8mlRf2RKA53KWCrRymeC7fWI8NRELGu5BJtQoxKtTOl2OhCLRHEZcJJL/x9ZNoKZlh6CaHYpsu+E7RRUTK6I47WXg8Gcrd9sp31ejpyCvL2NoU+ioehrBDv/42CVEPjTLeIs2798UsrvSoX0NmlzbKhPos1R/jrmkTRQiTaSote9m0q0dWfASPJXoo2k6HXvphJt3RkwkvyVaCMpet27qURbdwaMJP8/YupiOGKJgUwAAAAASUVORK5CYII=\" style=\"width: 77px; height: 20px;\" width=\"77\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIsAAAAoCAYAAADOkQm/AAAEpklEQVR4Xu2azctWRRjG3/cPUNJauZDQXISLBJMg3PZBQRAU5gciFGQGggvTctHCjzIXQtDnWlG3EVptWtSmMkgQ3FSIiLs+xD+grh/MDfPOe+Z5ztfzvDMv98DFc55zzpyZueaae+77PmdxwYsz0JKBxZb3+W3OwIKLxUXQmgEXS2uq/EYXi2ugNQMultZU+Y0uFteAMbBJBxuEH3OUuFhcLDCAUK4HKta7WFwUkxj4RhefE/4RXCyulSwD7+jK2XDVxeJCyTKwU1d+EK4Iu9yyuFJyDDysCz8JX4YbsC5uWVwvjQxc1tmHhOcF24oGiwVT9UC4kTRpodYtnf+r8gl5Qv1fI6RhI6vvceGe8GflY4y7/5r+nBKeDeMaJJY39ZCXBTxkCop7MiLstI7fC9fO6PdEhUS+oD7vD4StC/1/Ub9XwzGEfipw7VthrzDWojBxDqUtmxOZ8GALk/dFYx0kFgaDJYGwS6Hhg/r9QkAoKPIX4S3Bzg8d+Lzr2xgh74/QOI4eY0ZIF4TPwhi/C+fH6qOFqkOeN3HLmPBg5g0ciu4ZJJa4rf/CH4j7WvhYeGzIKAusa5NHYuoN4XshtqRjd5kFt33gQ//tIWBE8aqAnxJbydHEYkSy+kjYbEkaGjjmJdXxj4aWPqY5zjUgmPcF246G9qeU+hYmb1OHUv9zNLHERM56yzEr1pfgvqbZiKRd24r69qHEehYmn1PncCXSMppYYiJjBzBHCr4AMfuvQlfHFys2pPQxzdaeCXWSww7pJwV8ts0C4vxQ+GhIp+dQlzCZ/h7JtLVH5/E/Gc9L0T1LrHSbF4lM/m/hAccmEIOj+IpwXCCCqClKspUHoUQ+7Olp4R7EjLN7TdgqfBDGmquT08G8o6E+FnuZlZ4mlphEBs5+viPDAGK5L7wuYFlqEgsrj3S3lUd0kIbJpBM2CrG1jBdSky+QE8u8o6FpFpuAhYVCQfiUZVZ6mlgg8W/hdhAAD2kiMibF9r9axIIIjgoHBN6TUJq2W7ggt5Qm5whDiZzabNHG00pFQ/E8Nc1Z7wwuJBJGYkma/BbOPS2k+3VNYjHLYAsg9VuwrJ8I5F5yxaxEF8sy4XErcqmzgwtxZGxvCmsFspdxmBznW/CoyUU0hdEli4XJZ5u8I9wVvhJw6MyRi/MtbEtERtPC6N/D9D6l37EyvPNWTGexpPtoulLSfT23kkoWS5wGYELSVADW9PNopqalCiz7u1t14KfW0lkspLgPCzg2ePlp4gbL825go+m6EVWyWGwMvG0lE50m3iw0RgRN11MxYH1JVL5dsVVhTGyzB8LcZ7fcaQ5un5VSslj6jCdXB5/tvMB2tZreSGc5crH0kw+Wh3yLveLv95TKarlYuk8YW9VFge9B+ryH6t5iITVcLN0mwrK4TRES2y8JrdTX69ZCwXfPQiz2YVQtSbku00MCjlcZ9t2q1X1UB2xNY34g1aVfc7l3TLFA1jOCvS8hG8gHNj+vEgeQyIeXbbkyLcyey4TOspExxTLLfvqzC2DAxVLAJNTSBRdLLTNVQD9dLAVMQi1dcLHUMlMF9NPFUsAk1NIFF0stM1VAP/8HKS/3KS4kAo8AAAAASUVORK5CYII=\" style=\"width: 69.5px; height: 20px;\" width=\"69.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 58.5px; height: 20px;\" width=\"58.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, has only one root set, namely: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 96px; height: 20px;\" width=\"96\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; \"\u003enumRoots(2,10,4,1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.5px 8px; transform-origin: 90.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, two of the possible roots of:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 134px; height: 20px;\" width=\"134\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 126.5px; height: 20px;\" width=\"126.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                where:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 94.5px; height: 20px;\" width=\"94.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.75px; text-align: left; transform-origin: 384px 21.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eare \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"width: 166.5px; height: 20px;\" width=\"166.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In fact, there are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAACHUlEQVRYR+1WuUoFMRSd9wGCS2ship2goHY2Voq2goql4NqKilbiAipYuv2ACtqpuICNYqOFgp1LaeWC/oCeAzeScZLJvCHv8YoJHJLJ3OSenJvcJBeUWMmVGJ8gI+SKSKaQb4VqMeEX8O6a2PK/Ef0dQI38P0R9rNsmDRmJTACjQBNwnwehKtgOAkNAHTAF7AMvpjlchDjZvBBR4/MhREUOhMgp6jEbETV5HKEuGDUAD8Ac0CKDkhLqg/2OjFlCvQY4Q+1SSBGfRGM5D0JtsL0UeyozkIQM7QtBiGF+BCqAT1HWuF/S7KE0Cq1re46hmjU5tvX5VojqvGnOeKqoDjd3GfAq31aOvgkNw9OmeHtGvQ1MS/gUCfavAlvFCNkunPRqjjbQZvL7BqqBBYCqsRjD6VuhGzhS6WHEoAJDeqLZdKOdKlMnPfY/svq408X8diR2TAmdeuh8K6QTqrTu3CDQ7eph95cwfRP6kA1MheIIMWy8ZFlCmd83IeWIhEIr/6dW0QgtwvGMaeUWQhHivhViArwT5/2omQZM5QmdPP63QGshNzXnVkc/4kwc69k8Qtq3QvSp3/QmlVQKiRx5Dk5CiK/FM5GYY/jiW7GEQnXzLcRLljc+SZ0DPNrqatlDe1z6QlPFESIRPj2bDc55YfIZa7yPtND0oN0OlEvfBepr4Mq2oCQKOcTw+zsj5NIzUyhTyKWA63+2h1wK/QK6334lJE/2PwAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e possible root sets. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; \"\u003enumRoots(4,20,6,3)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6px 8px; transform-origin: 6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are no possible roots for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 185px; height: 18.5px;\" width=\"185\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 175px; height: 18.5px;\" width=\"175\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore in these cases the function should return: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 48px 8.5px; transform-origin: 48px 8.5px; \"\u003enumRoots = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.5px 8px; transform-origin: 62.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs an added challenge, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eonly those solutions with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/content/cody/about.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eCody program size\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85px 8px; transform-origin: 85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003e200\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e will be accepted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = numRoots(n,a,b,L)\r\n    n = 'number of unknown variables';\r\n    a = 'sum of the unknown variables';\r\n    b = 'alternating sum and difference of the unknown variables';\r\n    L = 'limit of the roots (i.e. all roots should be \u003e L');\r\n    c = 'the number of root sets';\r\nend","test_suite":"%%\r\n[n,a,b,L] = deal(4,20,6,3);\r\nc_correct = 16;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(4,20,6,-3);\r\nc_correct = 280;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(3,20,6,4);\r\nc_correct = 6;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n%%\r\n[n,a,b,L] = deal(2,10,4,1);\r\nc_correct = 1;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(10,55,10,-10);\r\nc_correct = 0;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(42,10,2,100);\r\nc_correct = 0;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n%%\r\n[n,a,b,L] = deal(10,25,15,-5);\r\nc_correct = '9825961376';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(25,50,25,5);\r\nc_correct = '0';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(8,88,8,8);\r\nc_correct = '159885';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(88,88,8,8);\r\nc_correct = '0';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(8,888,88,-8);\r\nc_correct =  '322979008681245';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(11,111,11,-1);\r\nc_correct =  '6367915454544';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(111,11111,111,11);\r\nc_correct = '2909165067998259047855867968538898760414304923603195356244648530663146995238036844997557527483252003388541616691119031429859046897494224647322949977583143171656492664325583077702371945252381217441222592230772490362933347417600378555600078275316289441596896000';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(1234,56789,1011,12);\r\nc = numRoots(n,a,b,L);\r\ns = [sum(c) histc(c,50:55) sum(c\u003c58) sum(c\u003e47)]\r\ns_correct = [127146 260 249 257 231 226 247 2428 2428];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('numRoots.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)\r\nassert(mtree(filetext).count\u003c=150)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-07T05:06:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-18T14:33:46.000Z","updated_at":"2023-02-07T05:06:35.000Z","published_at":"2023-02-02T11:44:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the tasks that Matlab is very good at, is in solving systems of linear equations. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem we shall tackle a system of linear \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Diophantine_equation\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDiophantine Equations\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in which the roots are limited to certain range.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the number of variables \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epositive integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a root limit, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(n,a,b,L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that outputs the number of posible integer root sets of the following system of equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2+x_3+x_4...+x_{n-2}+x_{n-1}+x_n=a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2+x_3-x_4...+(-1)^{n-1}x_{n-2}+(-1)^{n}x_{n-1}+(-1)^{n+1}x_n=b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e        with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2,x_3...x_{n-1},x_n \\\\ge L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (2,10,4,1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the system of equations: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2\\\\ge 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, has only one root set, namely: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2)=(7,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(2,10,4,1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (4,20,6,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, two of the possible roots of:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2+x_3+x_4=20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2+x_3-x_4=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2,x_3,x_4 \\\\ge 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eare \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2,x_3,x_4)=(5,4,8,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2,x_3,x_4)=(10,3,3,4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In fact, there are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e possible root sets. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(4,20,6,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are no possible roots for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (10,55,10,-10)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (42,10,2,100)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore in these cases the function should return: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eAs an added challenge, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly those solutions with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/content/cody/about.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody program size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e200\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e will be accepted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57745,"title":"Easy Sequences 100: One-line Code Challenge - 100th Digit of 100th power of an Integer","description":"Given a integer , write a function that computes the  digit of . If  has less than  digits just output a NaN.\r\nFor example if , the function should output: . \r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nImporting libraries is not allowed.\r\nRegular expressions, base conversion and string manipulation are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 245.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 122.833px; transform-origin: 407px 122.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126px 8px; transform-origin: 126px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that computes the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33.5px; height: 19px;\" width=\"33.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e digit of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 19px;\" width=\"25.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 19px;\" width=\"25.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.5px 8px; transform-origin: 55.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits just output a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 100px; height: 18.5px;\" width=\"100\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should output: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 78px; height: 18.5px;\" width=\"78\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 102.5px 8px; transform-origin: 102.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImporting libraries is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 248px 8px; transform-origin: 248px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, base conversion and string manipulation are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = digpow100(n)\r\n    import java.math.BigInteger\r\n    s = arrayfun(@(a) char(BigInteger(num2str(a)).pow(100)),n,'uni',0);\r\n    d = cellfun(@(a) str2num(a(100)),s);","test_suite":"%%\r\nn = 25;\r\nd_correct = 6;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 1:20;\r\nd_correct = [repelem(NaN,9) 0 4 3 0 1 1 1 3 8 4 0];\r\nassert(isequaln(digpow100(n),d_correct))\r\n%%\r\nn = 41:50;\r\nd_correct = [4 1 0 6 1 1 1 6 5 0];\r\nassert(isequaln(digpow100(n),d_correct))\r\n%%\r\nn = [111 222 333 444 555];\r\nd_correct = [0 2 3 3 6];\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 12345;\r\nd_correct = 8;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 123456789;\r\nd_correct = 0;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nimport java.math.BigInteger\r\nn = randi(10000,1,10)\r\nf = @(a) char(BigInteger(num2str(a)).pow(100));\r\nd_correct = [];\r\nfor a = n\r\n    if a \u003c 10\r\n        d_correct = [d_correct NaN];\r\n    else\r\n        b = f(a);\r\n        d_correct = [d_correct str2num(b(100))];\r\n    end\r\nend\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nfiletext = fileread('digpow100.m');\r\nnot_allowed = contains(filetext, 'import') || contains(filetext, 'str2') || contains(filetext, 'num2') || contains(filetext, 'dec2') || contains(filetext, 'base2') || contains(filetext, 'sprintf') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-06T03:48:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-03T04:05:24.000Z","updated_at":"2023-03-06T03:48:34.000Z","published_at":"2023-03-05T17:27:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that computes the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100^{\\\\text{th}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e digit of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e has less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits just output a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = [9,\\\\ 10,\\\\ 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should output: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[\\\\text{NaN},\\\\ 0,\\\\ 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImporting libraries is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, base conversion and string manipulation are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57730,"title":"Easy Sequences 97: One-line Code Challenge - Sequence with Constant Difference","description":"While answering Problem #57725, I noticed a pattern that immediately led me to a solution, namely: the -th difference of the sequence is constant. In that problem's case the constant is 6:\r\n    diff(A,4) == [6 6 6 6 ...]\r\nwhere  is the sequence.\r\nGiven an integer  and a vector  that enumerates the first  elements of , write a function that outputs the -th element of , such that the -th difference is a constant:\r\n    diff(A,k-1) == [c c c c ...]\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nTo encourage vectorization, for and while loops are not allowed\r\nRegular expressions, string manipulation and curve fitting are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 335px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 167.5px; transform-origin: 407px 167.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhile answering \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57725\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem #57725\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    diff(A,4) == [6 6 6 6 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e that enumerates the first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e elements of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that outputs the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th difference is a constant:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    diff(A,k-1) == [c c c c \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40px; transform-origin: 391px 40px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewhile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eloops are not allowed\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = nthElement(V,n)\r\n    x = A(n);\r\nend","test_suite":"format longg\r\n%%\r\nV = [1 2 3 4 5 6]; n = 10000;\r\nx_correct = n;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [790 1303 2033 3034 4366]; n = [10 100 1000];\r\nx_correct = [18511 32160346 256563524446];\r\nassert(isequal(arrayfun(@(i) nthElement(V,i),n),x_correct))\r\n%%\r\nV = [12 23 34 56 78]; n = 6:10;\r\nds = diff([V arrayfun(@(i) nthElement(V,i),n)],length(V)-1);\r\nd_correct = -22;\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = [123456 234567 345678 456789]; n = 10000;\r\nx_correct = 1111122346;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [123 456 789 101112 131415 161718 192021 222324 252627 282930]; n = 11:18;\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\ns_correct = sum(x)\r\nds = diff([V x],length(V)-1);\r\nd_correct = 2170350;\r\nassert(isequal(sum(x),s_correct))\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = sort(randi(100,1,10)); n = (length(V)+1):(length(V)+20);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(~any(diff([V x],length(V))))\r\n%%\r\nV = sort(randi(1000,1,10)); n = (length(V)+1):(length(V)+10);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(isequal(diff(V,length(V)-1),diff(x,length(V)-1)))\r\n%%\r\nfiletext = fileread('nthElement.m');\r\nnot_allowed = contains(filetext, 'str') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'fit');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-25T18:40:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-25T12:35:50.000Z","updated_at":"2023-02-25T18:40:33.000Z","published_at":"2023-02-25T18:35:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile answering \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57725\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem #57725\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    diff(A,4) == [6 6 6 6 ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e that enumerates the first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e elements of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that outputs the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th difference is a constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    diff(A,k-1) == [c c c c ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eloops are not allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55500,"title":"Easy Sequences 71:  A Nonlinear Function with Quadratic Domain","description":"Consider the function:\r\n                     \r\nThe outputs of this function are fed as domain to another function:\r\n                    \r\nwhere , is the Gamma Function.\r\nGiven the values of , , , and a limit , find the all values of, so that  and . For example if , and , the only integer values of  that will satisfy the above criteria are:\r\n                    . \r\nPlease present the final output as a unique row vector sorted ascending. \r\n-----------------\r\nNOTE: Some MATLAB's built-in math functions may only give approximate values. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 347.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 173.75px; transform-origin: 343px 173.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.75px; text-align: left; transform-origin: 320px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"104\" height=\"19.5\" style=\"width: 104px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe outputs of this function are fed as domain to another function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"153.5\" height=\"35\" style=\"width: 153.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31\" height=\"18\" style=\"width: 31px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gamma_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGamma Function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 31.5px; text-align: left; transform-origin: 320px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e find the all values of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, so that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"18\" style=\"width: 35px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37\" height=\"18\" style=\"width: 37px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOAAAAAkCAYAAACQVDZDAAAAAXNSR0IArs4c6QAACCtJREFUeF7tnQWsLEUQRc/HLRAkwd01uLu7u7u7u3twCO6uwd0lwd0lSHCH4E4Ovyd/M8zKzOzs7tvflbwElpnunuq+3VW3qppBRIkaiBromgYGda3n2HHUQNQAEYBxEUQNdFED9QA4GvBDnXFtAFzZxTH3atcjAz/XGdwmwKW9OvDUuBYEHq0z1umANwfId3RjmLsAp2R0/DUwTtaAmgFwIeDL1ItfAN924+t6vE91OU3GGI8Ebh1gADwLWDPjW94Hfuvxeejm8ATZ2KkBTA1cXBSAEwKfdPOL+qDvC4CHBxgA3cXn7APd98InzAw8GAHYvamIAOye7nuh574DoL7WeICn8xTAZMARwD+9oO2MMQxtAJwXeBvQ76laxgBc4I9V3VFo37U2CvBajv76DoBLBaUfBYwEXAOsm0MhnX50aAHgbMC+wNrADMDrFSpaknBD4ADgdmDbCvuyaTf7HYDdgK2By3L013cATL79bmBpYHtA0qBXpd8BOCOwFyDTm0hVANT6WQc4EJgydHZOhQAcF9gG2CecfHa5cQQgjAB8BowJzA4836voA/oZgFMBEwMvAHuEE8mpqAqAK4eT9Q/gLWB4oCoAjg4sCjwFaFbfGNZYBCAwB/AM8DkwCfB7BGDbNGAcsAgLunwwB6sEYO1HPgHMUyEAa/uSc/g0AnCISnYCTgPOCzZ521ZfBQ318wlYqy5983vCD1WdgLX9GdpZuEMANL6XxMPjCRgC2ysGR/yKCkDTziYjANupzSFtRQBWo9emrer3aXpq/5tl8E7TN7r7QARgNfqPAMzQ61jAWsD8gClrfwEXAeuF32WUysZslgHuCs64DNywwArAFoGQeQ+4KpAf7UybGg7w1J0rfJf/7gZwLnBvgzVWFIDDtGnd/p2znaI+YDRBsxXdsTDEcsCZwYE/O+QMuohOCnmFskrjAz/lXBDpx82tNP5zPHAwcHoAxHPATMDO4YWDAJ9th7gojTu669rvj6FRY5CrhbStl+p0VBSAtwArlRz8I8AiOduIAPy/wnreBzQ4KR28eTjxaj/B4OwxgL6awdMyYsLziyEQvwqwBHBd6lQ9IVDiViZorpZlSK3+uByQ+DmjZvAjAt+FZACBclsEYCRhMtZA5SegWSiafPUYyROB3YFNgUvKoC8EXxOfz+CoMZqHUm2uDtwQfjNG9VGJPjU5rWS4Glg/I91towByzdBf2wzAEsMu9Wo8AQfQCTg98GQ4BaSeswiRp4OJ1o5asuQ0slbxWODojKWmv5nUK5q390vB5ThBALhpSLMALxdsp6gJWrC70q9FAA4gAF4byBVNzP0zpl6SwowF/wRg2YTp8wPZ8j1gFsZXGX2amG2qksSIqWpFRR/y8GBalvHFIgCLzkDj94Z6FlQ2UBNQMUv8gwx9GSzXd9IM3bPkPOhzfRwKHgWZBExafMYk4MlDbmLRKnSTvN8NpJGJvvq3RSUCsKjmIgD/ywKvV5B7WADB/cCSGbrSJH01/C5TeFPJeagFvACzOjstif9nbqKhkKLmZ3Jy2770+n0lxl4UgJEFjQBsCECBt3ig5zX5akW20vCAsTlPk7JkiG3vCpzcoPzI2jBPZK+FMIlWE6WoLFDDrJp3aoijqEQAFtVcBGBDAH4ITBRMS03MWtk7BOINwkteSGIIyllTlQvGBS0x0dxrJncCywLbAcYZ04A/NZi7WwH6ilniyWboIH3PTfrZaYE3wo9uMl4pkBYTACyJ0b9tJEUB2EwfVf33TpEwrc5Fve/M4wNaP2jSvnP1ZwHF9WQc8AFgsRCCkKJXzA6xcNEY3DfA9SFp2kJGfUBLOqyWVgxf6KOZUnYooElbT7zoJiFc0iahwX7bNui+ZYO7VwSoQXoZVPu+o0F/ntre/uWkGYBPn/Cyq5I0bjARgIMVaanQzUGnZig1qhrPMxf1pkmrxCLgZgn5MvXe8uYacs69bCqva6IrloSz8t5wV1kcMAm+q6ALQwhC1lFQuTAFnVkwlg3pk0lk+M+JGBM0szwRr5cwjSxLVGIyoZa9eBoqnsBmpniSeuoa8sgSNwZT4wzMK4JLVraRrBE2EON7EklOnmld+qIWhQrMVqq+h5YT0JDQfkGhq9aAMa3jInORbsN512py87YsyaoIawSzxE1ZkCZiqqQHQx6p3VyOC5X/rb5fGQD9+B2BzRhcIKtJoN/3ShiZVxoKTIkYQxTpHdHT0/CFNV3KfEGZ9T5MUsXA+KSAYQh9Ps1JT1WD8c1MC09mi0YlcJRWYoT2acW9O62pdJrTZt74l6SjNZuIfgagG5pXULgp6e8noolvcoIbqhtyGhxF5sK2dQe8rc2kDjflRNyQ3SAfB55NTYhWjBlMSSjJuztl51sRDwg3apnwZPP2Pb/NE9jsJ5n5RlIZAFv5gFaecUf0Y0yyTooeW3mv6DP6bWbuzF20gZzv9TMAc6rif493ei4sNDY+7D0ynZKeB6CEh7uSJ00nRP9P0Jvf2QmJAKyv5U7OhWSfiSOe2Hl9wDLrpBQAszpu59X0pnsZWpAcscavatGk1KzQp6vnMxQdQ7yaPp/mqpyL9Egk1Vxn8g76jFVJ266ml1mUFMkS7Xt9sLLijVOHBPayE7dv66j7Z8ikih3QMEtyU1daNzK4+qsDQUYNpFbWWA09taPGsuq5qB2786LPpy9aj6Rr17zItNb6ikm7kneZobZu/t+Rkr7L5oe2qjw3lbzFqa22HZ/Lp4FOz0Wn+2tZG90EYMuDjA9GDfSrBiIA+3Vm43cNCA1EAA6IaYqD7FcN/Au8HElD53CvrgAAAABJRU5ErkJggg==\" width=\"112\" height=\"18\" style=\"width: 112px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the only integer values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that will satisfy the above criteria are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"266\" height=\"18\" style=\"width: 266px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output as a unique row vector sorted ascending. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-----------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Some MATLAB's built-in math functions may only give approximate values. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xs = intXs(a,b,c,n)\r\n  xs = a + b + c;\r\nend","test_suite":"%%\r\na = 1; b = 1; c = 1; \r\nn = 50;\r\nxs_correct = [-7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 6];\r\nassert(isequal(intXs(a,b,c,n),xs_correct))\r\n%%\r\na = 1; b = 2; c = 1;\r\nn = 500;\r\nxs = intXs(a,b,c,n);\r\nss_correct = -1;\r\nassert(isequal(mean(xs),ss_correct))\r\n%%\r\nas = 1:25; bs = -(101:-3:1); cs = primes(100);\r\nn = 1e4;\r\nxs = unique(arrayfun(@(i) sum(intXs(as(i),bs(i),cs(i),n)),1:25))\r\nxs_correct = [-13 -10 -8 -4 -3 2 4 7 11 16 19 49 52 55 67 73 93 101 114 125 204 270 294 345 614];\r\nassert(isequal(xs,xs_correct))\r\n%%\r\na = 10; b = 2; c = 101;\r\nn = 12345;\r\nxs_correct = [-35 -34 -31 -30 -25 -24 -19 -17 -11 -7 -6 -2 -1 0 1 3 4 8 9 14 15 16 23 30 33];\r\nassert(isequal(intXs(a,b,c,n),xs_correct))\r\n%%\r\na = 11; b = -31; c = 41;\r\nn = 1e6;\r\nxs = intXs(a,b,c,n);\r\nss_correct = [313 1165 130];\r\nassert(isequal([sum(xs(2:2:end)) sum(abs(xs(11:11:end))) floor(mean(abs(xs)))],ss_correct))\r\n%%\r\na = 131; b = -117; c = 119;\r\nn = 1e7;\r\nxs = intXs(a,b,c,n);\r\nss_correct = [13473 148];\r\nassert(isequal(floor([sum(abs(xs)) std(xs)]),ss_correct))\r\n%%\r\na = 13; b = -17; c = -19;\r\nn = double(intmax);\r\nxs = intXs(a,b,c,n);\r\nss_correct = [9102 9119 9142 9160 9193 9225 3 -14169663];\r\nassert(isequal([xs(4000:5:4025) mode(abs(xs)) sum(xs(xs\u003c0))],ss_correct))\r\n%%\r\nfiletext = fileread('intXs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":255988,"edited_by":255988,"edited_at":"2022-09-07T15:09:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-09-07T05:56:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-06T07:12:19.000Z","updated_at":"2022-09-07T15:09:06.000Z","published_at":"2022-09-06T19:29:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = ax^2+bx+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe outputs of this function are fed as domain to another function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=\\\\sin\\\\left( \\\\pi\\\\ \\\\cdot\\\\ \\\\frac{\\\\Gamma(y)+1}y{} \\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gamma_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGamma Function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e find the all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\\\\in\\\\mathrm{Z}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, so that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \\\\le n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[a, b, c]= [1,1,1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the only integer values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that will satisfy the above criteria are:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs=[-7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output as a unique row vector sorted ascending. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-----------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Some MATLAB's built-in math functions may only give approximate values. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52804,"title":"Easy Sequences 29: Odd proper divisors of odd proper divisors","description":"The number  is special. It has odd number of proper divisors:  . Furthermore, if you take any of its proper divisors, say , it too has odd number of proper divisors: . The numbers  and , have similar property as . \r\nGiven a limit , find how many integers , have similar property as 210, namely, the integers should have odd number of proper divisors and all its proper divisors have odd number of proper divisors, as well. \r\nThe number , does not qualify because it has even proper divisors,  in total  . The number  also doesn't qualify because although it has proper divisors, some of its divisor, like , have even number of proper divisors. \r\nNOTE: A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number , which is considered a proper divisor of itself.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 237px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.5px; transform-origin: 407px 118.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155px 8px; transform-origin: 155px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is special. It has odd number of proper divisors:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 288.5px; height: 18.5px;\" width=\"288.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Furthermore, if you take \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eany\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83px 8px; transform-origin: 83px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of its proper divisors, say \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it too has odd number of proper divisors: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 126px; height: 18.5px;\" width=\"126\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA+klEQVRYhe2WTQ2EMBBGn4c6wAAGVgEKcICDdbAW0FAJeMBCNWBh99CS8NPpEqYQDn3JXAjvS5uZQqFQKDyDV6j6ZneFAXrgu6kJ6C50o1RB3gYu63OBKzIADmgXz2r2u24yu1Ea/A6lnr8XoTajK2JJ99mwnolcrkiPn4MUgxCqcVXMocPNrogLoWeOsMaNUoVAx//25HRF5pNyZocaN4rBD+OZ/mtcEQuMIfxON0qH7/2Zn6TGjdIqAjXu8xfTHAisiR9hjSu+POEvVxIGP6jbUI2bXMyI/3ZI5dgfY42bXEzqgiXdazSuiA0rP1KW9XdF4xYKhUIhxg+zAZ+7e7/gtwAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.5px 8px; transform-origin: 81.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have similar property as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.5px 8px; transform-origin: 87.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find how many integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have similar property as 210, namely, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe integers should have odd number of proper divisors and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eall\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 196.5px 8px; transform-origin: 196.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e its proper divisors have odd number of proper divisors\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29px 8px; transform-origin: 29px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as well. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 172.5px 8px; transform-origin: 172.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, does not qualify because it has even proper divisors, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e8\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in total  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAScAAAAlCAYAAAAA5S/+AAAGvklEQVR4nO1c7ZHqMAzcHuiABmjgKqACOqADOrgWqIES6IEWqIEWeD/CDsLYjj8kHy9oZzJzwyWxvZLXku0YcDgcDofD4XA4HA7HQnFIXD9/WSmHw/FfQlVP7gAuAM7BtdOoqcPh+CqEOnIGcMMkUNW4w6Mkh8NhhzP+SJw2Hc+W4udxjSgrxMaw3A2ebQuvI4C1Ubksuxasm2W9wrJa6rkWz1tDlrWqeG6FtO23AH51q9ntaz2cDhenHYArgFNLoQVYYSLtHlw3AHujMkNsH2VatHGFqS1h+3idDcoE6u22xmQHhuaHx/Nn6It2r81l2w6i3nvUCUcJto+yYnYrEe9D5Fl5aQprj69pcDpMnEKjWHTcNfJk3qE/soSQBrVo40jnBNrstsHEwRWvQrQS79oq1a/X5sfEPXs8O6CWQP3O1POGvECNHphafU2L0yHi9PuoGCtn1XHPmJxfTspv8D6qanWMVB2s2kjnHBUBtthNClCsnj/iXRqdvsfmbNc1URfaUmNAY7tlKrTCM8JgPS+ZdzD61I7mYmj1NU1Oh6d1Vh13i4nMVMogRwGrlJLOczEqZ4/50dUKpdyR51w92Rl7+emxuYxCUh1lJ57vTUUvmIQphjAiSpV1g33kT7T4mjanixGnE/IqvxJl35TLBiaiyQlHB+02UvhqJ1E1UGo3OmcuApBRTU87emwuo8FUJL0W9/SIwgbzEY9M+WJt2on/jVjgafE1bU4XI04lKwcUDW1xYipDIi3ESY44MgXYYYxQldhtK+5LRQnAqxP37IvrsTmj2/vMOyi218Y6AhMvc+mRTHdj94aT6DdM7bcQqlZf0+Z0MeJUAjqq9sThMXinhTjFVniko1ovf5fYTaZRuc4oO2JOxDSQsnlpFC3nEC3TaclJaMuYWMjrCN0BqtXXtDn9KnHKTdS2gqtZcgSzSuvkXpaYA1lO9JfY7STuKxWnXPqngZjNmYLXdiRLfilAqfSP+4X2eOWZl+aqIlDvaxacfo04Mde9Qm8E5DJ2mJpYiVOIHV4nUm+wS/FK7CadrlScLOb/iJTNa8ovbVMvOA9X2hnXeBeppo5ciDlfs+D0a8SJKYemg50RT0tGiRMwOYjM9a0ctFac5uZCRohTyuayI5WuPlqKE1e5WrYJyJTPcnAC8r5mwelXiBONrznXlNtzMlKcgNeNiFY7xGvFKecb1iunLCNlc9mR5viaW0XTADtr67yhrKP13GPK1yw4/QpxOmFSfK1Rhfl1KjoYLU7AMy2w6uz/W1qXs/knpXX0pZ5VS7k8P2KDbszXPK1rwB7vE9Y94LaBI9IfRDL0PYvfrPemcBn/L8WpZbXOwg9KbN7SkSy+CbxCZ2MlfW6EOKV8TZvTRYsTPw3QdCrZsWou6/ayXj37cXIoaYec/ygVJ+0dz6U25wpUaUfS3pnP+Rut9rOeI85TS/maNqeLFScLYcLjfbGDscJDskg+f7NcSQGeo5nVvqESu60L75MRlubyfI3N5S71kghLc8uDtjABz8hpxKdNKV/T5nSR4hTbexRiAztD/uWck9VenFK7se25CO4k7tGaB6y1uYzeUtGG3LujmS6VCFONHTkoWO8ZI1K+ps3px4rTClPlD6iLfnhcx9xq0QXve18O0PkcZE6catvGA8ZSYkrnTK2SaLSt1G65nc7A60pd6JyjbT73xQBXlWIi2spp+DVBDDu8RiU88C33zhzfI32th9PYuz5SnMIjL0qIpZNekD4wXR56Rsh0RCPimROn2rbJzW8HvBqVne6SeI9W22qepwPG7mVKF3PekTYHXpfFw7LkF/ahn7dyKs85StUzFBr5HWIsMuQ8X6oTj/Q1oJ3TGIaKk5xrmNupHe5+nZtLoZOWTlBvg2fD//ekfHPiVNs2ubpB7g6YnJwfgKZGIY221diNkB2RdZs7bGykzcN3yKNX1njO4aSeqeU0dlJn6pLpWWwB5ojJJjzLKpcCjvQ1ooXTVF3MxWmHiaTY5HEq3NyIZ0hKDqn3x64T3gmmsTUmFn+RJ7a2bcA7h3TQ0qNdW9rWYjeJHzy5OD/+zjnmaJsTTH1O4t498jzVcLqtqOcZ7/M1a7zySP5LVuZG+xrRwmmI4WldC2IGs8IP7JbjY1hy23owkpceOKd2+HhxKjmoSxNzB5hpYslt68FoXnrgnNrho8Vpg/zkmzaOGHcM6pLb1oPRvPTAObVFlzjt8f7phtbeoRUmw486L3uHcSHvktvWg9G89MA51UXqM7BmcYpd1juhHQ7H8uB64nA4HA6Hw+FwOBwOh8PhcDgcDkcM/wAwZLX6P4KfpgAAAABJRU5ErkJggg==\" style=\"width: 147.5px; height: 18.5px;\" width=\"147.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAAB6ElEQVRYhe2Xa7HCMBCFPw91EAMYQAEKcFAHdVAL1VAJ9YAFNNRC749mb5dMHpvC5c/NmekMkH2d5HSzQENDQ8N/hAO6Ez5X/9Tionxr82YLmoDNJ7DgDjyBGRi8/wr0hcKcsh0C38Wvn0LHQUIeCxnxGYPfe//7QpzQhaPocF3WVk4QurHvyg14YCcjBT8TBS/EieJ9Np8zF3sq1JDFgI1Mx75zqWJhl18s1sWQ4+rXV2vhMVjJ9MoutbtO2WjCV8q+YvO0Fh6DlYyWY07Xcnq6qE75PohLdCR/6iZYyYhNSQYLcdK62YRNQBrAkzc6GtjIaM3XkNGS6ng93ZVdWjf/eeID942FjNZ8DZk+WAsJSbzUe1SNWjJzRbyQDKQJWS9sc3ILmaUQbyRPRvKNHM2i1OnM+KbMpAlI0S6w3zg35/3iL7uZjid5YjLVne4r94yMI1Yy4ZwlkkpJaeYDp2MlMxnt9OUo0DK1tP/Yu2aClYwu6F5ZkIUMCd8qWMnAIaFUR5NOFpuqRWapjdAjz+kpoIaMU0WFtnqqjmle8qRmMxlkS/dYtjh5sTefsAT9R0oIOY6LMHdXyMk9eN2M3sebOTHSOB94iTwTZc123mb2PrP/bpGHY980nXPgzfuloaGhoaGhweMHP8kF0IkWOc4AAAAASUVORK5CYII=\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 142px 8px; transform-origin: 142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e also doesn't qualify because although it has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAdklEQVRYhe2OwQmAMBAEp4d0kAbsw0bsIB3YQmqxB1uwF/0YCHiPyGEU3IHjXrMMCCG+RQTCC645loEdGDq6F0I1Vq511OOajEA6/3pz1OM2kRyjHldBClKQghSkIAX9MigCWzWaOrnm2AwsxmVgesgVQghRcwBVnXRb64UZ7QAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eproper divisors, some of its divisor, like \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have even number of proper divisors. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340px 8px; transform-origin: 340px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is considered a proper divisor of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = oddDivs(n)\r\n  s = n;\r\nend","test_suite":"%%\r\nn = 100;\r\ns_correct = 61;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 60794;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nns = 10000:50000;\r\nss = arrayfun(@(n) oddDivs(n),ns);\r\nss_correct = [729580926 12160 15197 18242 21278 24310 27360 30401 7020];\r\nassert(isequal([sum(ss) ss(10000:5000:40000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 123456789;\r\ns_correct = 75052724;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = intmax;\r\ns_correct = 1305513583;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = double(intmax)*10;\r\ns_correct = 13055135057;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = double(intmax)*200;\r\ns_correct = 261102702413;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nfiletext = fileread('oddDivs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T04:54:26.000Z","updated_at":"2026-02-24T15:31:17.000Z","published_at":"2021-09-27T12:53:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is special. It has odd number of proper divisors:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,3,5,6,7,10,14,15,21,30,35,42,70,105]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Furthermore, if you take \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eany\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of its proper divisors, say \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e70\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it too has odd number of proper divisors: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,5,7,10,14,35]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have similar property as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find how many integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have similar property as 210, namely, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe integers should have odd number of proper divisors and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eall\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e its proper divisors have odd number of proper divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, as well. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, does not qualify because it has even proper divisors, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in total  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,4,5,10,20,25,50]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e108\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e also doesn't qualify because although it has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eproper divisors, some of its divisor, like \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have even number of proper divisors. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is considered a proper divisor of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52866,"title":"Easy Sequences 36: Hyperbolic Lattice Points","description":"The graph, shown below, of the hyperbola: , passes through four positive lattice points:.\r\n                                            \r\nIt can be shown that those  points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point  on the xy-plane where both  and  are integers.)\r\nGiven the integers  and , write a function that counts the number of positive lattice points that the hyperbola: , passes through.\r\nNOTE: The trivial point , is not to be included in the count.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 510px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 56px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe graph, shown below, of the hyperbola: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"35\" style=\"width: 61px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, passes through four positive lattice points:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be shown that those \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"19\" style=\"width: 39.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e on the xy-plane where both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are integers.)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 56px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven the integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a function that counts the number of positive lattice points that the hyperbola: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"35\" style=\"width: 61px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, passes through.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe trivial point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"19\" style=\"width: 36px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is not to be included in the count.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numPosLat(a,b)\r\n  y = x;\r\nend","test_suite":"%%\r\na = 2; b = 4;\r\nn_correct = 4;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 12; b = 28;\r\nn_correct = 20;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 100; b = 1000;\r\nn_correct = 36;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 123; b = 456;\r\nn_correct = 48;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 12345; b = 54321;\r\nn_correct = 48;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\nas = floor(linspace(201,1234,100)); bs = floor(linspace(401,5678,100));\r\nns = arrayfun(@(i) numPosLat(as(i),bs(i)),1:100);\r\nss = floor([sum(ns) mean(ns) mode(ns) median(ns) std(ns)]);\r\nss_correct = [4750 47 48 32 43];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\na = 35153041; b = 12117386241;\r\nn_correct = 975;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = floor(double(intmax)/7); b = floor(double(intmax)/3);\r\nn_correct = 1944;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = floor(double(intmax)/5); b = double(intmax);\r\nn_correct = 8;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\nfiletext = fileread('numPosLat.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-06T10:44:57.000Z","updated_at":"2026-02-24T17:29:27.000Z","published_at":"2021-10-06T19:09:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe graph, shown below, of the hyperbola: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\frac{2x}{x-4}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, passes through four positive lattice points:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{(5,10),\\\\ (6,6),\\\\ (8,4),\\\\ (12,3)\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"293\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"309\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be shown that those \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on the xy-plane where both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that counts the number of positive lattice points that the hyperbola: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\frac{ax}{x-b}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, passes through.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe trivial point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is not to be included in the 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Sequences 98: One-line Code Challenge - Ternary Operator Function","description":"Ternary operation is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\r\n    y = (p \u003e q) ? m : n;\r\nwhich means that y is assigned the value of either m or n, depending on whether the statement (p \u003e q) is true or false, respectively.\r\nUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\r\n    if p \u003e q\r\n        y = m;\r\n    else\r\n        y = n;\r\n    end\r\nBut that is 5 lines of Matlab code versus just a single line in C!\r\nIn this problem we are required create the function ternaryFunc, which takes on the following parameters:  data values a and b; a conditional function C, that outputs true or false, and functions T and F which are applied to a and b, depending on the value of C(a,b). We can write the function as follows:\r\n    function x = ternaryFunc(a,b,C,T,F)\r\n        if C(a,b)\r\n            x = T(a,b);\r\n        else\r\n            x = F(a,b);\r\n        end\r\n    end\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nUse of if, while and switch statements is not allowed.\r\nRegular expressions and string manipulation are not allowed.\r\nUse of variable length arguments is not allowed.\r\n-------------\r\nHINT:  As an exercise you may want to first solve Problem #44243.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390px; transform-origin: 407px 390px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Ternary_conditional_operator\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eTernary operation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    y = (p \u0026gt; q) ? m : n;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich means that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is assigned the value of either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003em \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, depending on whether the statement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e(p \u0026gt; q) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis true or false, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 100px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 50px; transform-origin: 404px 50px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eif \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ep \u0026gt; q\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        y = m;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eelse\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        y = n;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBut that is 5 lines of Matlab code versus just a single line in C!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this problem we are required \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecreate the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eternaryFunc\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, which takes on the following parameters:  data values \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e; a conditional function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that outputs true or false, and functions T and F which are applied to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, depending on the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eC(a,b)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We can write the function as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 140px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 70px; transform-origin: 404px 70px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = ternaryFunc(a,b,C,T,F)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eif \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eC(a,b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e            x = T(a,b);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eelse\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e            x = F(a,b);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 100px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 50px; transform-origin: 391px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eif\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ewhile\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eswitch\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e statements is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions and string manipulation are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse of variable length arguments is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAs an exercise you may want to first solve \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44243\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eProblem #44243\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = ternaryFunc(a,b,C,T,F)\r\n    if C(a,b)\r\n        x = T(a,b);\r\n    else\r\n        x = F(a,b);\r\n    end\r\nend","test_suite":"%%\r\na = 20; b = 2; \r\nC = @gt;\r\nT = @(a,b) a ^ b;\r\nF = @(a,b) b ^ a;\r\nx_correct = 400;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\nC = @le;\r\nx_correct = 1048576;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 123; b = 456; \r\nC = @lt;\r\nT = @(a,b) round(sind(b/a),4);\r\nF = @(a,b) round(sind(b*a),4);\r\nx_correct = 0.0647;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\nC = @ge;\r\nx_correct = -0.9511;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 'A'; b = 'A'; \r\nC = @eq;\r\nT = @(a,b) log(a/b);\r\nF = @(a,b) log(a*b);\r\nx_correct = false;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 1000; b = 2000; \r\nC = @gt;\r\nT = @(a,b) char(a + \" is greater than \" + b);\r\nF = @(a,b) char(b + \" is greater than \" + a);\r\nx_correct = '2000 is greater than 1000';\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = repelem('1',5); b = repelem('2',100); \r\nC = @(a,b) all(lt(a,b(1:length(a))));\r\nT = @(a,b) arrayfun(@(i) i,1:str2num(a));\r\nF = @(a,b) arrayfun(@(i) i,1:str2num(b));\r\nx_correct = 1:11111;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 1; b = 0; \r\nC = @lt;\r\nT = @(a,b) a * length(1:1/b);\r\nF = @(a,b) b * length(1:1/a);\r\nx_correct = 0;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = randi(1000); b = randi(1000); \r\nC = @le;\r\nT = @(a,b) a * length(1:b/a);\r\nF = @(a,b) b * length(1:a/b);\r\nif C(a,b)\r\n    x_correct = T(a,b);\r\nelse\r\n    x_correct = F(a,b);\r\nend\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\nfiletext = fileread('ternaryFunc.m');\r\nnot_allowed = contains(filetext, 'str2') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'if') || contains(filetext, 'while') || contains(filetext, 'switch') || contains(filetext, 'vararg');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-29T18:12:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2023-03-01T19:53:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-26T08:27:07.000Z","updated_at":"2026-02-27T16:09:27.000Z","published_at":"2023-02-27T08:38:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Ternary_conditional_operator\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTernary operation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    y = (p \u003e q) ? m : n;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich means that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is assigned the value of either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, depending on whether the statement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p \u0026gt; q) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis true or false, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    if p \u003e q\\n        y = m;\\n    else\\n        y = n;\\n    end]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut that is 5 lines of Matlab code versus just a single line in C!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem we are required \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecreate the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eternaryFunc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which takes on the following parameters:  data values \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e; a conditional function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that outputs true or false, and functions T and F which are applied to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, depending on the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC(a,b)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. We can write the function as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    function x = ternaryFunc(a,b,C,T,F)\\n        if C(a,b)\\n            x = T(a,b);\\n        else\\n            x = F(a,b);\\n        end\\n    end]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eif\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswitch\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e statements is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions and string manipulation are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse of variable length arguments is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eAs an exercise you may want to first solve \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44243\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem #44243\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52978,"title":"Easy Sequences 44: Finding the Smallest Number whose Cube is divisible by a Factorial","description":"Given a integer , our goal is to find the smallest integer , such that  divides .\r\nFor example, for , , because , (since ), and  is the smallest number that has this property. Please present the value of  in modulo  (a prime number).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 83px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, our goal is to find the smallest integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAkCAYAAABxE+FXAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAH6ADAAQAAAABAAAAJAAAAACmdlxhAAACLElEQVRYCe2VO0iVYRjHD3KKvISkbkIODhKSpCKUOIhDpdjgUoOTEEFLOdjsoosgETRFDo62BCJ0gVra3AoXLchugxZidIPs9vuf877w8J73++JwPC19D/zP87zP/7m81+/kcplkO5DtQOU70EOJG6Cz8lLlVagl/Dv4DXZBDfhncopOauxxPNa5WjPKB80ag3FhWK3m74NmO8G4qsPDVPdbLt1Q1W6R4rpoapy46vBsbI0WBt0Oz9F3HdmGPgfawQp4BGLyFqfO+nWMTPLNQyjRbtu4C55Afw64PseF6r6LWw6JtHEH5Hng3+ke9hFwBfwA18E94Cd3GTsmt3Eq5maMTPMdgPwElPwYjIGv4DSQXAW++dmCp/Rn2sVcK6WKnqSnpo+Ev6HPsBfBJfAQSLqKqvD71NjW1NFJyjpzJcwAv7JX2LfkNLKOLX7N+ELzjIvRQsqSVaJ98w3sOpN91HC6nEmiPxTVaE0KiPmbcf4EvvlQEHTRcFpdkuiZ6dImHW007wJe3/hBJGLJ8d/Q+vdKk4U0MsYpwTcfDgK0ig+O95cvCKls+MYV30bng1K9jtPkphynyQ462yrlngSHrDPNPgbpVx3ecOVNGl6f3lmgT6/O14q+Ey+Aar0E9eCvYouPRqLn8PnJPcH+COyb9ykDJk7xJzyRpu+4pC/o2GUawf/LxbxD94OYNOHcAmq8CQ6CfRG9X304YpOzDTQB7YCOIJNsB7Id+E934A+h4YEZjRgqXgAAAABJRU5ErkJggg==\" width=\"15.5\" height=\"18\" style=\"width: 15.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e divides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 53px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"18\" style=\"width: 43.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, because \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"54.5\" height=\"20\" style=\"width: 54.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, (since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"32\" style=\"width: 59px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the smallest number that has this property. Please present the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e in modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (a prime number).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = SCDF(n)\r\n    k = mod(10*n,1000000123);\r\nend","test_suite":"%%\r\nn = 6;\r\nk_correct = 60;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 10;\r\nk_correct = 2520;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 100;\r\nk_correct = 29482652;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 1234;\r\nk_correct = 27609071;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 123456;\r\nk_correct = 34685960;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 22222222;\r\nk_correct = 27608842;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = floor(double(intmax)/100);\r\nk_correct = 12770769;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nns = floor(double(intmax)./(20001:20050));\r\nks = arrayfun(@(n) SCDF(n),ns);\r\nss = floor([mean(ks) mode(ks) median(ks) std(ks)]);\r\nss_correct = [27662018 2442880 25739266 15619436];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('SCDF.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-28T11:43:38.000Z","updated_at":"2026-03-24T12:58:42.000Z","published_at":"2021-10-29T14:06:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, our goal is to find the smallest integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e divides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, because \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6!\\\\ | \\\\ 60^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, (since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac_{60^3}_{6!} = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smallest number that has this property. Please present the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e59999999\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (a prime number).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56458,"title":"Easy Sequences 80: Sum of the n-th Row of Fibonacci Square Triangle","description":"We shall call the following arrangement of Fibonacci numbers, as the Fibonacci Square Triangle:\r\n                        \r\nwhere:  and  for .\r\nWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. ), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\r\nIn this problem, we are required to find the sum of the n-th row of the Fibonacci Square Triangle. For example for the 4th row, the sum is:\r\n        \r\nSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\r\nTherefore, for the 4th row, your program output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 445px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 222.5px; transform-origin: 407px 222.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe shall call the following arrangement of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, as the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFibonacci Square Triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 150px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75px; text-align: left; transform-origin: 384px 75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"167\" height=\"19\" style=\"width: 167px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"20\" style=\"width: 38px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this problem, we are required to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efind the sum of the n-th row of the Fibonacci Square Triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. For example for the 4th row, the sum is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"429.5\" height=\"21\" style=\"width: 429.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for the 4th row, your program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM0AAAAmCAYAAABnPx8oAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAzaADAAQAAAABAAAAJgAAAAD4EainAAAKEUlEQVR4Ae2cC9BVVRXHUcjQpMikTBIyiRgLMtO0UBJqSEcdtcgpDQVfNY72nCZKJ22G6KGMaTbBQE4k2kPJamzCcjSSyAYnTUnLHjAo2sOykPJBYr8fnF179nfOuefe796Pc/Osmf+3915r7X3WXvux9t6XYdiwhhoPNB5oPNB4oPFA44HGA40HauSBXQpsORj+1wtk18L/VIGsYTce6DcPLMHgaQVGz4C/KZWNSBlZeXfSieAO8MeMF5K/h0yTNh74P/DAr+jDPkk/xlOeDFwHA6go0kxFczU4CXxnQK1qjL1R+zz4A5ifU2U0vFfm8ItYdyN4MhFqv1HxcDAFrAdrwFrwOKhKu6J4ChgJllatNER6Z/KdI8GlYF3ON18Nb48cfh7rrzAdj5QcK8f8MDAK3A70o/5sh16O8vvBAvAIqAu1moupne+FsQg4P3+XCovKOvAZcGKRQgW+i802dH4efQGm8qoYlzQyhvLKrP5dpCvAn7Lyg6SHglbkYnkXuA9ox3JQJ7IPW4G2zcwx7MXw3Eiq+vCqnDbcLB4Dm8F3wc/Av4FtfgmMAK1oPxQWg6eA9SaAOlGruZja6qJpux+DXTRnZx/1w3mLxrD3aKSjXhnuRx7TvhRcGNZZCELENPUuJt9I8w6QR+opuwfE363TonkettnvYF/eopkXyYNeWXoq+jFdREF9j+ATI8Eh5P8JlP0YFEWysciuBOnCrdOiaTUXMX8AlS6aEQPUB88wpF3Wohl399HAO9M1wGODA5TSl2HsCb6dCD5H2QFzh7wYhLqmc8BBYBKw/k1gC4jpGAqzge2cDI4HdSN9qC+LyCh5DnBzWALyjq+whx0BnARGgRtBIP1zQVbQT/HG5LicC74K3gzOB/oqpStg3AvOAkaxXswnmu2YqszFjhtPK06F4QQ8MRW0KOu0n4P14AlgG2tASur8EOyWCqLyGPLhmOAxJZB3mG3Atq8OzCT9ZCZX58JElhZnRbrLU+FOKp+Q2fTryLaZiS3HUNY/b034afFyGPrh+4nAo5h8cUAis7g7CNHGTe35MktoHbLQ3oQSvaESVZ2LefaURhp3q27SRTR2CDgNeEbOo5Ewt4DTgbtfEfkIMRxsBF7sAx1FJhzHfhuYSeoZNtCHQqYg1ZY60T4YsxS4qXyxxLB9kenvm0t09NOsTL4i0TsqK7vwNmT5ODGCGaWlvcAcMyVUNz9WmYsl3SkWdXPRGJ0+Dnwxu634k9sj0FuQP1yio+idmTw9mvlaFGhTyCTpfVHZAXeC9Qt5zHFc5oJnSoz+CrJPl8gVvQnYdxeGkSWQF/cQObzPPB0ESerRK9BrQqYP0qpzsaOudGvRjOLrV4O7gUejwdIYGpieNZLukHHof0HBh7bCjyOdZ9t+oPMw0mOXx4OHumBw2HhW0ZZHrEBVfKhuXKdffNjtuRh89t+0W4vmSlp8KXgPcMIOlrxLDQfugumdKB5Id8wieiQS9MOAH4i9Rumvgesj2zvNlh3NYh86yYo2n37zob7q9lwc4P9uLBp3M+8wHwNxOB/wsTYYYYe8gTrbknrro/Kx5J0ceeTLWiCfb+tMPohcA/4Mzu+SoW+knbFA/+nHmGIfyj8uFkb5fvKhZvdiLkbu2JEd7KJ5Gc0sBj8CZZfWHV+r9ndv1IqOZrYQX/KNIB5nUtoDxgERc2OUr2N2PkZNAbNBfKwcjK1h4zFSG7FjcjHcEjHOI29kT2lyxKi7D3sxF6Pu/y87mEXjDr8MeFmdk6UkgyaPZj4XeoRYldPabfBEoGvJTMsK2uRArwB7ZjyTn0b5umWnY9BHwCUg7tdg7NQPs7IG9EUefQZmeGg4nPwyECLyC8mfAS4AgVaHTA1T+6v93Z6LbXV1amaAE7iIHGiNDDtaqudRQ3l6J0n10vJNWb2rUkFUNhrdk+n5DfEQeDTLu+AC/zfky+hohEF3eZliD2SjadMd/E6wW07758ILts3MkRexPJqFeuOKlOC/L9JT/ynwe7ANhN/ZQjvvhldGtyMMuhPKFHsg6/Zc9CHGvuT2Y0SHHZhEvQXACelx4m0gpVEZw4kR5P8iX7abvgj5jKxe0Q6p2AvqoeA04GA6Mf4B/DHwJ2A8mAek1TuSWv69HKt8zLgMTM+x8HUR7/Xk3VElXykf3p7L/xM2sjsQuyiLaBECo/AHgP50zFw0NwLvWLcCj7pSXf3Yq7m4o9dt/G0VaYxAYVdpJ3VAyuhMhLbnAsjbecvqBtlwMg+AYNfbg6AgPTrSXV6g0yv2XdG3g71V0tklBrmwXCi2EzaOEvVC0TlZG7bjIm1FOyvS9GIu9iTS6EhDeBntGgmD7tMRLy8bdkh3Oo8KnZAd9lIoGa3SH0e3C2ryR78E3+SZ5AII0UV50NX/RXQYgv0yYVm0Lqov3x8+P5opbCWdk+XrmPRqLrbd11aRpkqD7d5pPJo5QDqhVXQo+r5HmCeyNjaR7lWkGPF3ZqSJzMjNdnKnWUhL+rBKdMj9KMzrsjZsx58SqtDOijRVbGt3LpZGmjgaVPl4L3VOoHHvWN57VnbwIRedg/1c4GCfDv4GWlG8k7fSfQ4KxwFfpsJLU6s6Qym3L9omdRplPkzd0MYq8pfYWAVqx4/7095c8NoK7dZOxUlaFwpHsx9gkAunHZqB8jLgsexx4Hn8ZlCFXhIpjYzyeVkn4vGZ4Bek08HmrFyH5A0YMS4zpN1F4ybgg8TZWf1bSU8G4UiYsQuTqn70NLAW7AI8rnuPdez6nob6eOYxyjuMEaLV02bs3LEUFgIH1rp3goNAVXoFir8E1hV/Aa8CeWRUDjYGfSdVL6nd49mlGKNtvmpWJTdOj6j3A+u66cwHPqhUIfU+CIJPTB0To3IeXQgz1r03T6nLvK4ez4ps68ai2Zg555aij0T8uZmu95FREb8o6xFiDXCxeA/yGy42d68q5GJ7AITFFg+ivPXAc21K18GIdS9OFbpcPiP63rQKbW/I9BdU0J2CzlLg8719ehBcAcIjAtmW9Fk0toDYJyHvC+i6nBYOh/dYVMdo44bUS2pnLmpH6Z2myNBuLJqitvP442EeCQ7OE+bwFsObB44FRqmhpIl87FTg5DhlKD9c4Vv6UHi/a0XezTyOuTD9PajqhoPqoGk0LRwIfDwwwtWN+mLR1M1prexZhIJHOZ9mG+rMA26UT4JPdFa9p7VKF02vw2JPe7YTGtdf7s6zgRfYzaCh9j0wmSqrwSqgP/uKmkXT3nCdhfpJwOPr99qr2mhHHlhJ/lvAf6Huw0Nf0YgW1s5BfkSis5byNxPes6X4DTp6Pajy+8+zxSed9NNNZ0MnFXtQx41wUtJulUeXpMqO/xwjvIKk6ZIB2g2j8UD/euAGTE/neCjv37/daixvPNB4oPFA44HGA40HGg80Hmg80Hig8UDjgcYDjQcaDzQeaDywMzzwH268nN22z2DtAAAAAElFTkSuQmCC\" width=\"102.5\" height=\"19\" style=\"width: 102.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumFST(n)\r\n    s = [4791 4791 4];\r\nend","test_suite":"%%\r\nn = 4:8;\r\ns_correct = {[4791 4791 4] [5971 7175 6] [1932 2536 9] [1632 8113 12] [3605 8865 15]};\r\nassert(isequal(arrayfun(@(i) sumFST(i),n,'uni',0),s_correct))\r\n%%\r\nn = 10;\r\ns_correct = [3152 5555 23];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 50;\r\ns_correct = [2682 1525 533];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = [1928 7575 2111];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 500;\r\ns_correct = [8201 1625 52351];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 600:100:1000;\r\ns_correct = 742673;\r\nassert(isequal(sum(arrayfun(@(i) sum(sumFST(i)),n)),s_correct))\r\n%%\r\nn = 100:10:1000;\r\ns_correct = 7865124;\r\nassert(isequal(sum(arrayfun(@(i) sum(sumFST(i)),n)),s_correct))\r\n%%\r\nn = 1234;\r\ns_correct = [3836 6419 318495];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 123456;\r\ns_correct = [1647 8064 3185286664];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = [1345 9375 208987849238];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nfiletext = fileread('sumFST.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":255988,"edited_by":255988,"edited_at":"2022-11-17T19:00:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-04T19:35:14.000Z","updated_at":"2026-03-23T18:26:25.000Z","published_at":"2022-11-08T12:04:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe shall call the following arrangement of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, as the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci Square Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)^2\\\\\\\\F(2)^2,\\\\ F(3)^2\\\\\\\\F(4)^2,\\\\ F(5)^2,\\\\ F(6)^2\\\\\\\\F(7)^2,\\\\ F(8)^2,\\\\ F(9)^\\\\ F(10)^2\\\\\\\\F(11)^2,\\\\ F(12)^2,\\\\ F(13)^2,\\\\ F(14)^2,\\\\ F(15)^2\\\\\\\\F(16)^2,\\\\ F(17)^2,\\\\ F(18)^2,\\\\ F(19)^2,\\\\ F(20)^2,\\\\ F(21)^2\\\\\\\\....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)=F(2)=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(i)=F(i-1)+F(i-2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u0026gt;2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, we are required to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efind the sum of the n-th row of the Fibonacci Square Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example for the 4th row, the sum is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_4 = F(7)^2+F(8)^2+F(9)^2+F(10)^2=13^2+21^2+34^2+55^2=4791\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for the 4th row, your program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4791,\\\\  4791,\\\\ 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44394,"title":"How to calculate the length of a triangle's side given two angles and one side","description":"You are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\r\n\r\nWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\r\n\r\nThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.","description_html":"\u003cp\u003eYou are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\u003c/p\u003e\u003cp\u003eWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\u003c/p\u003e\u003cp\u003eThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.\u003c/p\u003e","function_template":"function a = triangles(alpha,beta,c) \r\n    \r\nend","test_suite":"%%\r\nalpha = 30;\r\nbeta=40;\r\nc=1;\r\na_correct = 0.5300;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 1;\r\nbeta=70;\r\nc=0.5;\r\na_correct = 0.0100;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 40;\r\nbeta=100;\r\nc=0.2;\r\na_correct = 0.200;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 1;\r\nbeta=1;\r\nc=11;\r\na_correct = 5.5;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n%%\r\nalpha = 37;\r\nbeta=62;\r\nc=3;\r\na_correct = 1.8300;\r\nassert(isequal(triangles(alpha,beta,c),a_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":4,"created_by":157578,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":133,"test_suite_updated_at":"2017-11-02T14:53:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-01T17:15:24.000Z","updated_at":"2026-03-30T19:14:20.000Z","published_at":"2017-11-02T14:10:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a triangle with angles alpha, beta and gamma and sides a opposite alpha, b opposite beta and c opposite gamma.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function ‘triangles’ which, given alpha, beta and c calculates the length of the side a.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe angles alpha and beta are given in degrees. You should round your answer to two decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47295,"title":"Find Logic 13","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 102\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 99\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 103\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\nassert(isequal(logic(x),102))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),103))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),97))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:07:30.000Z","updated_at":"2026-02-14T07:02:11.000Z","published_at":"2020-11-05T07:07:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 99\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 103\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47370,"title":"Find Logic 25","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(11) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(15) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(22) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic in problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 6;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":234,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T13:48:01.000Z","updated_at":"2026-02-14T13:45:20.000Z","published_at":"2020-11-06T13:48:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(11) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(15) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(22) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic in problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47345,"title":"Find Logic 20","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 7;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 7;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),9))\r\n\r\n%%\r\nx = 6;\r\nassert(isequal(logic(x),2))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":365,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T05:30:27.000Z","updated_at":"2026-03-17T20:15:27.000Z","published_at":"2020-11-06T05:30:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43301,"title":"Calculate inverse matrix in m by n matrix ","description":"  x=(1:10)'\r\n  y=roundn(2*x+7*rand(size(x)),-1)\r\n\r\na*x=y\r\n\r\nEstimate a using inverse matrix calculation. This is principle of linear regression.","description_html":"\u003cpre class=\"language-matlab\"\u003ex=(1:10)'\r\ny=roundn(2*x+7*rand(size(x)),-1)\r\n\u003c/pre\u003e\u003cp\u003ea*x=y\u003c/p\u003e\u003cp\u003eEstimate a using inverse matrix calculation. This is principle of linear regression.\u003c/p\u003e","function_template":"function a = reginv(x,y)\r\n  a =\r\nend","test_suite":"%%\r\n  x=(1:10)'\r\n  y=3*x\r\n  a=3\r\n\r\nassert(abs(reginv(x,y)-a)\u003c0.001)\r\n\r\n%%\r\n  x=(1:10)'\r\n  y=3*x+2\r\n  a=3.2857\r\n\r\nassert(abs(reginv(x,y)-a)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2018-07-19T15:35:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T09:36:59.000Z","updated_at":"2026-01-02T15:53:13.000Z","published_at":"2016-10-10T09:36:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=(1:10)'\\ny=roundn(2*x+7*rand(size(x)),-1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea*x=y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEstimate a using inverse matrix calculation. This is principle of linear regression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43334,"title":"Solve the system of linear equations","description":"  4x - 2y  +6z=8\r\n  \r\n  2x + 8y  +2z=4\r\n  \r\n  6x + 10y +3z=0\r\n\r\nInput is each coefficient of polynomial. For example,\r\n\r\n  a=[4 -2 6 8;2 8 2 4;6 10 3 0]\r\n\r\nFind x,y,z. Output should be\r\n\r\n b=[x;y;z]\r\n\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003e4x - 2y  +6z=8\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e2x + 8y  +2z=4\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e6x + 10y +3z=0\r\n\u003c/pre\u003e\u003cp\u003eInput is each coefficient of polynomial. For example,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ea=[4 -2 6 8;2 8 2 4;6 10 3 0]\r\n\u003c/pre\u003e\u003cp\u003eFind x,y,z. Output should be\u003c/p\u003e\u003cpre\u003e b=[x;y;z]\u003c/pre\u003e","function_template":"function b = solvepol(a)\r\n  b=\r\nend","test_suite":"%%\r\nx=[4 -2 6 8;2 8 2 4;6 10 3 0];\r\ny_correct = [   -1.8049\r\n                 0.2927\r\n                 2.6341];\r\nassert(abs(sum(solvepol(x)-y_correct))\u003c0.01)\r\n\r\n%%\r\nx=[     9    10     3    10\r\n       10     7     6     2\r\n        2     1    10    10];\r\ny_correct = [ -2.6456\r\n               3.0127\r\n               1.2278];\r\nassert(abs(sum(solvepol(x)-y_correct))\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":"2016-10-15T04:33:08.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-11T14:18:34.000Z","updated_at":"2026-04-01T07:49:35.000Z","published_at":"2016-10-11T14:18:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[4x - 2y  +6z=8\\n\\n2x + 8y  +2z=4\\n\\n6x + 10y +3z=0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput is each coefficient of polynomial. For example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a=[4 -2 6 8;2 8 2 4;6 10 3 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind x,y,z. Output should be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ b=[x;y;z]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47240,"title":"Find Logic 6","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 212.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 106.31px; transform-origin: 174px 106.31px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic and Make a function by finding logic from this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 29\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 66\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFunction logic(x) will return 'x' th term of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 3;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 3;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 66;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 514;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":402,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T06:26:21.000Z","updated_at":"2026-02-27T04:52:00.000Z","published_at":"2020-11-04T06:26:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic and Make a function by finding logic from this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 29\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 66\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFunction logic(x) will return 'x' th term of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47350,"title":"Find Logic 21","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 72\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value equal  to 'x'th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 45;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 72;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":261,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T06:12:12.000Z","updated_at":"2026-03-17T20:16:52.000Z","published_at":"2020-11-06T06:12:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 72\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value equal  to 'x'th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52824,"title":"Easy Sequences 31: N-N's Sequence","description":"We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number  appears  times. The first few elements of this sequence are as follows:\r\n                        \r\nAs you can see,  appears  times,  appears  times,  appears  times, etc...\r\nWrite a function that output the number  occuping the  position.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times. The first few elements of this sequence are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 518px; height: 18.5px;\" width=\"518\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs you can see, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, etc...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that output the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e occuping the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 26.5px; height: 18px;\" width=\"26.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = nnPos(k)\r\n    n = k;\r\nend","test_suite":"%%\r\nk = 1;\r\nn_correct = 1;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 20;\r\nn_correct = 6;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 1000;\r\nn_correct = 45;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nks = 12345:12345:246900;\r\nns_correct = [157 222 272 314 351 385 416 444 471 497 521 544 567 588 609 629 648 667 685 703];\r\nassert(isequal(nnPos(ks),ns_correct))\r\n%%\r\nk = 2000000;\r\nn_correct = 2000;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 123456789;\r\nn_correct = 15713;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax;\r\nn_correct = 65536;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax('int64');\r\nn_correct = 4294967296;\r\nassert(isequal(nnPos(k),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-28T18:15:10.000Z","updated_at":"2025-12-22T17:00:59.000Z","published_at":"2021-09-28T18:16:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times. The first few elements of this sequence are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left \\\\{ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8 ...\\\\right \\\\} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you can see, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, etc...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that output the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e occuping the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\\\mbox{-}th\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52779,"title":"Easy Sequences 25: Product of Series","description":"The function 'P(n)' is defined as the series product:\r\n                            \r\nwhere 'T(n)' is the triangular sum:\r\n                            \r\nIt can be proven that P(n) is convergent, with:\r\n                            \r\nWrite a function that outputs the integer value of 'n' when '3 - P(n)' first becomes less than or equal to a given tolerance 't'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function 'P(n)' is defined as the series product:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"124.5\" height=\"46\" style=\"width: 124.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ewhere 'T(n)' is the triangular sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"184\" height=\"19\" style=\"width: 184px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be proven that P(n) is convergent, with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 30px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"83.5\" height=\"29\" style=\"width: 83.5px; height: 29px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003efirst\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e becomes less than or equal to a given tolerance 't'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(t)\r\n    n = N(t); \r\nend","test_suite":"%%\r\nt = 1;\r\nn_correct = 4;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.5;\r\nn_correct = 10;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.01;\r\nn_correct = 598;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.007;\r\nn_correct = 856;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.00032;\r\nn_correct = 18748;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nts = 10.^[-1:-1:-8]*3;\r\nns = arrayfun(@(t) N(t),ts); \r\nss_correct = 222222205;\r\nassert(isequal(sum(ns),ss_correct))\r\n%%\r\nt = 0.0000000026;\r\nn_correct = 2307692306;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nfiletext = fileread('n.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-24T21:04:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-24T20:12:14.000Z","updated_at":"2025-12-22T16:55:44.000Z","published_at":"2021-09-24T20:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function 'P(n)' is defined as the series product:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(n)=\\\\prod_{k=2}^{n}\\\\frac{T(k)}{T(k)-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere 'T(n)' is the triangular sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(n) = 1 + 2 + 3 + 4 + ...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be proven that P(n) is convergent, with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lim_{n\\\\rightarrow \\\\infty}P(n) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e becomes less than or equal to a given tolerance 't'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52921,"title":"Easy Sequences 40: Quadratic Congruence","description":"Quadratic Congruence is a modular equation of the form: . \r\nIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (), and a modulus base (). Using these data, create a function that outputs the pair (), which are the 'primitive' solutions to the quadratic congruence.\r\nFor example consider the congruence: ,  the solution is , since:\r\n                                    , and\r\n                                    .\r\nNOTE: A primitive modulus to base , can only have values from  to . This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 235px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117.5px; transform-origin: 407px 117.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eQuadratic Congruence is a modular equation of the form: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 167px; height: 19.5px;\" width=\"167\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297px 8px; transform-origin: 297px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 18.5px;\" width=\"79\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and a modulus base (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eUsing these data, create a function that outputs the pair (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 75px; height: 20px;\" width=\"75\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e), which are the 'primitive' solutions to the quadratic congruence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example consider the congruence: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 157.5px; height: 19.5px;\" width=\"157.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  the solution is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAlCAYAAAD/Tp9wAAACAklEQVRoge2ZXbGDMBBGjwcc1AAGUFAFOMABDmqhGioBD7VQDVjgPiw7DZSU8LMJt8M3sy+ZJmxOks1uCqdOnTJW7bEipVMrtetcOuAJNCMr9/A0ssZzaIAWgbNYHf9zd4SqISGYvDcL5Yh/U3YHLjP9k4G59mM8NozhU4Ychc5jTcAYScC4jluAqfFDCfU7CZiGt5N7g1Ho1cZxooOpgRdyo1mAqRAwczFkTlHB5E4/3TV7g1HoBbJ71ioamAxxWj9mAabkM548+/alkKKBuTO8DSzAvPAH3JZl/kYBc0WcdnMWq6NU9N+7MQ3qGjiOOZgLslrjUsEKzFglw5ymJexYmYNpkGM01R4DDAgIvQU7wiZsCkav5qkVigkG3js3eearV7OvFooNBmTn6nGakwkYvZrv+As53dqN02ZVUKq0PksGpuB7reIz692jfr0CfmsCJmf68Wf8EKSrp22rHFkg3TFTl8FYyZ4dUsaYkFzmsGAypCCsCYs9We+Pr3i8EH4jqX+HBKOrqzYHx03iaoYpguYxz4BxXP8OCebBEMxcXHDfeDTA1khp0Pb9lxSSycDcZj6eI3A0UIcEzNLpoxl3zbq3maSP4aFK8bfM4cHk+MsKSx0aTM6ygLmnNoGp+Ez1t761qjIkDu013jf5SpbVYKbMOnu10C/N5dSpU6d+V3/phxOZDm3/bAAAAABJRU5ErkJggg==\" style=\"width: 35px; height: 18.5px;\" width=\"35\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, since:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 292px; height: 19.5px;\" width=\"292\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 292px; height: 19.5px;\" width=\"292\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA primitive modulus to base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, can only have values from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e0\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38.5px; height: 18px;\" width=\"38.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xs = quadCong(cs,m)\r\n    xs = cs;\r\nend","test_suite":"%%\r\ncs = [1,5,6]; m = 3;\r\nxs_correct = [0,1];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [1,5,6]; m = 7;\r\nxs_correct = [4,5];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [6,-7,-5]; m = 11;\r\nxs_correct = [5,9];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [35,76,33]; ms = setdiff(primes(10000),primes(100));\r\nys = arrayfun(@(m) sum(quadCong(cs,m)),ms);\r\nss = [sum(ys) floor([mean(ys) mode(ys) median(ys) std(ys)])];\r\nss_correct = [5752615 4777 57 4151 3465];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\ncs = [10,-131,391]; m = 6373;\r\nxs_correct = [3195,5103];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [253,-1420,672]; m = 30103;\r\nxs_correct = [3927,8215];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [528,26711,283500]; m = 198733;\r\nxs_correct = [37227,174629];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\ncs = [4545,13092,-69741]; m = 1000121;\r\nxs_correct = [821876,933449];\r\nassert(isequal(quadCong(cs,m),xs_correct))\r\n%%\r\nfiletext = fileread('quadCong.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-10-17T05:04:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-12T12:11:53.000Z","updated_at":"2025-11-28T12:16:40.000Z","published_at":"2021-10-16T17:40:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eQuadratic Congruence is a modular equation of the form: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eax^{2}+bx+c\\\\equiv 0\\\\  (mod\\\\  m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this exercise you will be given a vector containing the coefficients of a quadratic polynomial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs =\\\\left[ a,b,c\\\\right]  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and a modulus base (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUsing these data, create a function that outputs the pair (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs=[x_{1},x_{2}]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e), which are the 'primitive' solutions to the quadratic congruence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example consider the congruence: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^{2}+5x+6\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  the solution is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4,5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4^{2}+5\\\\cdot 4+6= 16+20+6= 42\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5^{2}+5\\\\cdot 5+6= 25+25+6= 56\\\\equiv 0\\\\  (mod\\\\  7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eA primitive modulus to base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, can only have values from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. This is a simplified problem, in which the quadratic polynomials given in the test suite, are all factorable, and the modulus base are all odd primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47385,"title":"Find Logic 28","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 21\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 38\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 33\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 69\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will written 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 21;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 21;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 22;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 38;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 33;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":200,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T17:21:56.000Z","updated_at":"2026-02-19T09:52:52.000Z","published_at":"2020-11-06T17:21:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 21\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 38\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 33\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 69\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will written 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43235,"title":"Calculate geostrophic current","description":"  eta0=0.01;\r\n  R=300;\r\n  f=0.01;\r\n  g=9.81;\r\n  x=-500:50:500;\r\n  y=-500:50:500;\r\n  [x y]=meshgrid(x,y);\r\n  eta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n\r\neta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\r\n\r\nhttps://en.wikipedia.org/wiki/Geostrophic_current\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003eeta0=0.01;\r\nR=300;\r\nf=0.01;\r\ng=9.81;\r\nx=-500:50:500;\r\ny=-500:50:500;\r\n[x y]=meshgrid(x,y);\r\neta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n\u003c/pre\u003e\u003cp\u003eeta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\u003c/p\u003e\u003cp\u003ehttps://en.wikipedia.org/wiki/Geostrophic_current\u003c/p\u003e","function_template":"function [u,v] = your_fcn_name(x)\r\n  eta0=0.01;\r\n  R=300;\r\n  f=0.01;\r\n  g=9.81;\r\n  x=-500:50:500;\r\n  y=-500:50:500;\r\n  [x y]=meshgrid(x,y);\r\n  eta=eta0*exp(-(x.^2+y.^2)/R^2);\r\n  \r\n  u=\r\n  v=\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\neta0=0.01;\r\nR=300;\r\nf=0.01;\r\ng=9.81;\r\nx=-500:50:500;\r\ny=-500:50:500;\r\n[x y]=meshgrid(x,y);\r\nvi=(g*eta0)/f*(-2*x/R^2).*exp(-(x.^2+y.^2)/R^2);\r\nui=-(g*eta0)/f*(-2*y/R^2).*exp(-(x.^2+y.^2)/R^2);\r\n[u,v]=your_fcn_name(x)\r\nassert(isequal(u,ui)\u0026isequal(v,vi))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T16:11:31.000Z","updated_at":"2025-12-08T12:29:58.000Z","published_at":"2016-10-08T16:11:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[eta0=0.01;\\nR=300;\\nf=0.01;\\ng=9.81;\\nx=-500:50:500;\\ny=-500:50:500;\\n[x y]=meshgrid(x,y);\\neta=eta0*exp(-(x.^2+y.^2)/R^2);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeta indicates sea surface height in each point (x,y). Calculate geostrophic current (u,v).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Geostrophic_current\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Geostrophic_current\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47320,"title":"Find Logic 17","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 281.524px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 140.762px; transform-origin: 174px 140.762px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,1) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,4) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a Function logic(a,b) which will return value according to problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = 3;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 1;\r\ny_correct = 3;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ny_correct = 5;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ny_correct = 11;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 5;\r\ny_correct = 23;\r\nassert(isequal(logic(a,b),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":2,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":457,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T15:48:34.000Z","updated_at":"2026-02-14T06:58:04.000Z","published_at":"2020-11-05T15:48:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,1) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,4) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a Function logic(a,b) which will return value according to problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43290,"title":"Calculate numerical integration.","description":"  x=0:0.01:1\r\n  y=@(x)x.^2\r\n\r\nUsing given two inputs(x and y), conduct numerical integration in x.\r\n\r\n(hint: trapz)","description_html":"\u003cpre class=\"language-matlab\"\u003ex=0:0.01:1\r\ny=@(x)x.^2\r\n\u003c/pre\u003e\u003cp\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/p\u003e\u003cp\u003e(hint: trapz)\u003c/p\u003e","function_template":"function z = integralx2(x,y)\r\n  z=\r\nend","test_suite":"%%\r\nx=0:0.01:1;\r\ny=@(x)x.^2\r\nz_correct = 0.3334\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n\r\n\r\n%%\r\nx=0:0.01:1;\r\ny=@(x)x.^3\r\nz_correct = 0.25\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T05:49:20.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-10T05:41:31.000Z","updated_at":"2025-11-29T14:58:18.000Z","published_at":"2016-10-10T05:41:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0:0.01:1\\ny=@(x)x.^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(hint: trapz)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47300,"title":"Find Logic 14","description":"Guess the Logic!\r\nlogic(1) = 100\r\nlogic(2) = 96\r\nlogic(3) = 105\r\nlogic(4) = 89\r\nlogic(5) = 114\r\nMake a function logic(x) which will return 'x' th term of sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54px 8px; transform-origin: 54px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 96\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 105\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 89\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43px 8px; transform-origin: 43px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 114\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\n%%\r\nfiletext = fileread('logic.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'elseif') || contains(filetext, 'switch') ; \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 96;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),89))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),114))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),127))","published":true,"deleted":false,"likes_count":7,"comments_count":1,"created_by":293792,"edited_by":223089,"edited_at":"2023-02-22T19:11:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":367,"test_suite_updated_at":"2023-02-22T19:11:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:18:24.000Z","updated_at":"2026-02-14T07:00:09.000Z","published_at":"2020-11-05T07:18:24.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 96\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 105\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 89\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 114\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47315,"title":"Find Logic 16","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 180\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 225\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 120-x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 120;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 225;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":4,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":393,"test_suite_updated_at":"2020-11-07T12:21:32.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-11-05T14:49:56.000Z","updated_at":"2026-02-14T06:59:02.000Z","published_at":"2020-11-05T14:49:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 180\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 225\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47410,"title":"Find Logic 32","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.476px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 155.738px; transform-origin: 174px 155.738px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = 27\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 54\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value equivalent to logic.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 3;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 18;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":206,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T12:03:44.000Z","updated_at":"2026-02-19T09:54:35.000Z","published_at":"2020-11-07T12:03:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = 27\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 54\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value equivalent to logic.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47365,"title":"Find Logic 24","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 341.429px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 170.714px; transform-origin: 174px 170.714px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 27\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5,3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(a,b) which will return value equivalent to logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = a-b;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 3;\r\nassert(isequal(logic(b,a),1))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\nassert(isequal(logic(a,b),27))\r\n\r\n%%\r\na = 5;\r\nb = 4;\r\nassert(isequal(logic(b,a),125))","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":211,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T12:07:22.000Z","updated_at":"2026-03-17T20:28:18.000Z","published_at":"2020-11-06T12:07:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 27\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5,3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(a,b) which will return value equivalent to logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53940,"title":"Easy Sequences 66: Fractional Part of Sum of Consecutive Powers over a Prime","description":"Given three postive integers, ,  and , create the function , defined as follows:\r\n            \r\nWhere  is the th prime and the symbol  is the  fractional part function of a positive real number, defined as follows: \r\n        If  then , where , is the 'floor' of .\r\nFor example for ,  and , we have:\r\n        \r\nTherefore, since :\r\n        \r\nPlease round-off the output to four decimal places, so in this case: .\r\nHINT: This is related to the Faulhaber's formula.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 355px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 177.5px; transform-origin: 407px 177.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven three postive integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 85px; height: 18.5px;\" width=\"85\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62px 8px; transform-origin: 62px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 181px; height: 45px;\" width=\"181\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.5px 8px; transform-origin: 77.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime and the symbol \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAlCAYAAAAqXEs9AAABj0lEQVRYR2NkGGSAcZC5h2FYOEgYGKrmQKwDxI+AeAVaKEcA+XJAfAWITwLxW1JigZQQAjmkGYgzgXg6EG8B4qdAfBHNQiUgXwOIfZDU1hLrMGIdBHLMDiA2AeJILKGCKxBAobUciM8AsSkxIUWsg9KBhs2AhkwWMQYjqQFFaTixHiHWQWVAAzuBuByIu0h0EEl6Rx1EKHRHQ2g0hLCEwMjIZdOg1QAppTQssEgqVInJZaC6CVT0g4AqsXUSUtSBqp3bxOon5CAvoEFLgPgdEAcDMXpFSijTwOT1gYy1UE4ekN6GSyMuB8EqRZA+UM1Oav2Fyz5QBe0OlcQa/cSE0CSoAQMaQsg+HFRpCOYwWC7LAArMJDbhQNXBor8NyK8mpJdQlMH0k1S4oVlKkt5RB41GGZYQGE1DhJLFyAghWOFGTr1Gk34Zcs/VG19tjRZ/yD1XD6AcwX4+sQUjyB70vv0yoNgzIL6H5ghQU0MaiGnat0evbM2AAqARjgEd/SCUm6giT0qUUcVCQoYMOgcBAAO3hiZP4FMsAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18.5px;\" width=\"18\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://brilliant.org/wiki/factional-part-function/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efractional part function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a positive real number, defined as follows: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 46px; height: 19px;\" width=\"46\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAAAlCAYAAAAwTGn2AAAFVklEQVR4Xu1cOcsVSxD1+wEGLpGBgUsgCApuIBoYuEdi8DQTFNzAUFFf5gJqJriBoetDMxVNNNDEDTQyUQNBI1f8Ac9zpBuaYWbu6e66y9zbA8XcO0zXqao+1TNT3TNT08pWItCxCEx1zN5ibonAtELaQoLORSCFtLPg5SrIYsgnyC0Dr9dAx2qn7wX2Hw10FhX5EWBfrzfqY9WaHb3wYkhLB05A9kMuQe5BPkPeqta0nEfdiyCbnX4S94iRbgPzJlYFB5OnkBie5ARrHhp/6IWnGkNSPYQsh+zslQk5VqPtEsgTp4N4ZdTNDGhG80GTVsJTSbsXjl92I+yBjCCoTQeNp9o1aedJJDIMioSnkvYwDDvjLtlnDY1sUuWNf4QTNg0Ar0DUR0AikWHwJLxCWsOIj6EqiUSGfkt4hbSGER9DVRKJDP2W8AppDSM+hqokEhn6LeEV0hpGfAxVSSQy9FvCK6Q1jPgYqpJIZOi3hDcI0tKQLxBfb2UddjrkWYuz41Y9oM/c/EQMi+hzIO8g3ww73VqVRKIaUD9ZFPpHXb+DGNTZKuH1g7SssW6DLIDMd5bNdvvr2G90vznj1VQ+syQtdeVuvYJd1U/MfyHsPE6QcNsKeQA5BTnmjo16SU8ikfPlIvZMxpWQGZBXkBUQJuzdgAtr8btpwJLwVNLSIE7fxsyGvXQdRuNZa+WMGp3xRD6N38cb2ERH30A4pUfy52z/5zR2bW9jzznx2C0kKBOX0+Abghj4jo3VO6jzJRIFxjBJv7r/7N//IJzd/B747JO3zgcJTyEts4fB5bYQol7OPGlpPIlKApKk7Ej+52jTNkVLknNUbstMpfOoJ3d7DAUpkyqetIzfVcgeCEcfJsAuyElI221Srt257SUSBSAhaTnA0b9DkOeQCxCSt21GVcLrRdotALnmwLZjry6OqWYcRxd2VsxGHbyd4OXmKOQORE2YGJx+nusTlwuMSNSYpA/t8s8BObam3D9LJAqMIl/uu/8crLg1XU3rfJHwmkjLAN90Whnw2PUGofEcYWMIX3XGTyHzeIotOR2d0zZMXMbgHORKokJ/1Uls/rfZUog66HgciUSBUf7KQn9nOomxWcJTRtrzDjWGeP4emE1T7we7PtKGif8joQPDziYZlsX0fs25HHhiV8xJJAqw3uO3f2bZl5CkEl4v0tKelHva0PiUDCeu1T3tMKoHtD9M3JQOzOSoSXOJRA7Jr4Xl39QklfAU0oYdoATfP/nnjLI+ABZP18OqHvChg9WS1A40YV2mEolEDsMvJ+VfhSd1pkl4KmljliaGxreVN9riaVmnHUb1IEzcttJeJqf63lwikbOCr139436zvJfy0Czh9YO0/rKeM8JYkrbvPVsDED48pt4eDcPuKqZEItfIX9FSn2GoRsKzJm34xJzzpN910vpSl8XkyDDJK5EIBobVopgJqKQksSZtaHzqrUGYcaM+zVlHqGqNOqZOOUyCJt9jomF15i/l1mBoI61fd0ADcl6T6fJI69cdMAZdf6NYHWn9uoPX8DknSSU865HWaqToMmmtYjAKeiQSGRoq4RXSGkZ8DFVJJDL0W8IrpDWM+Biqkkhk6LeEp5LWT0nmVARifCvfPYiJVv/OlUhkCC/hqaQNvzCTUxVQ/Au/MLMODWIXeSgY5RwtAhKJNFXSWRKeSloiVr/ldQPHwtdoJKsaTvKvn5RveeVE0b5t+EBc1f4TBw5CUspb7G9WHKqbf9OjlZcxpPUA/pWKuThQvppoT5RR0kgS7W4w6BeOpy61zNKbQtpRCmqxZQIjUEg7gZ3edZcLabvegxNo/x/Jg0o14VJOFQAAAABJRU5ErkJggg==\" style=\"width: 86.5px; height: 18.5px;\" width=\"86.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 23px; height: 18.5px;\" width=\"23\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the 'floor' of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36px; height: 18px;\" width=\"36\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.5px; text-align: left; transform-origin: 384px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; 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\" style=\"width: 430.5px; height: 35px;\" width=\"430.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.5px 8px; transform-origin: 210.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease round-off the output to four decimal places, so in this case: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152px; height: 18.5px;\" width=\"152\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This is related to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFaulhaber's formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FPSP(x,e,n)\r\n    y = FPSP(x,e,n);\r\nend","test_suite":"%%\r\nx = 10; e = 2; n = 6;\r\ny_correct = 0.6154;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 3; n = 50;\r\ny_correct = 0.6288;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 100; e = 4; n = 100;\r\ny_correct = 0.2495;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 250; e = 5; n = 200;\r\ny_correct = 0.1415;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 123; e = 6; n = 200;\r\ny_correct = 0.1292;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 10; e = 10; n = 300;\r\ny_correct = 0.7006;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 1234; e = 56; n = 789;\r\ny_correct = 0.8419;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nx = 3000; e = 300; n = 3000;\r\ny_correct = 0.6441;\r\nassert(isequal(FPSP(x,e,n),y_correct))\r\n%%\r\nxs = 20:2:2000;\r\nys = arrayfun(@(x) FPSP(x,x/2,x),xs);\r\nss = round([sum(ys) nnz(ys) mean(ys) mode(ys) median(ys) std(ys)],4); \r\nss_correct = [472.0982 numel(xs) 0.4764 0.2518 0.4704 0.2854];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('FPSP.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2022-01-20T12:19:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-19T18:18:26.000Z","updated_at":"2026-03-28T13:08:19.000Z","published_at":"2022-01-20T10:08:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven three postive integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,y,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(x,e,n)=\\\\left\\\\{ \\\\frac{1}{p_{n}} \\\\cdot \\\\sum^{x}_{i=1} i^{e}\\\\right\\\\}  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime and the symbol \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://brilliant.org/wiki/factional-part-function/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efractional part function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a positive real number, defined as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er \\\\in \\\\mathbb{R}^{+}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{r\\\\}=r-\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor r \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the 'floor' of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sum^{10}_{i=1} i^{2} = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_6=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=\\\\left\\\\{ \\\\frac{385}{13} \\\\right\\\\}  = \\\\{29.615384561538...\\\\}=0.61538461538...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off the output to four decimal places, so in this case: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFPSP(10,2,6)=0.6154\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is related to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Faulhaber%27s_formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFaulhaber's formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43278,"title":"Make roundn function","description":"Make roundn function using round.\r\n\r\n  x=0.55555\r\n  y=function(x,1)\r\n  y=1\r\n\r\n  y=function(x,2)\r\n  y=0.6\r\n\r\n  y=function(x,3)\r\n  y=0.56\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eMake roundn function using round.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex=0.55555\r\ny=function(x,1)\r\ny=1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey=function(x,2)\r\ny=0.6\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey=function(x,3)\r\ny=0.56\r\n\u003c/pre\u003e","function_template":"function y = myroundn(x,n)\r\n  y = \r\nend","test_suite":"%%\r\nx = 0.5555;\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.5555;\r\nn = 2;\r\ny_correct = 0.6;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.5555;\r\nn = 3;\r\ny_correct = 0.56;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 1;\r\ny_correct = 0;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 2;\r\ny_correct = 0.1;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 0.1111;\r\nn = 3;\r\ny_correct = 0.11;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 1;\r\ny_correct = 4;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 2;\r\ny_correct = 4.3;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 3;\r\ny_correct = 4.27;\r\nassert(isequal(myroundn(x,n),y_correct))\r\n\r\n%%\r\nx = 4.2736;\r\nn = 4;\r\ny_correct = 4.274;\r\nassert(isequal(myroundn(x,n),y_correct))","published":true,"deleted":false,"likes_count":30,"comments_count":3,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4518,"test_suite_updated_at":"2016-11-22T18:46:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-09T12:34:11.000Z","updated_at":"2026-04-02T02:10:47.000Z","published_at":"2016-10-09T12:34:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake roundn function using round.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0.55555\\ny=function(x,1)\\ny=1\\n\\ny=function(x,2)\\ny=0.6\\n\\ny=function(x,3)\\ny=0.56]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47400,"title":"Find Logic 30","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 371.381px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 185.69px; transform-origin: 174px 185.69px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 44\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 45\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 49\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 51\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 56\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(9) = 56\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(10) = 57\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 42;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 44;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 45;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 50;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 51;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 55;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":195,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T11:28:49.000Z","updated_at":"2026-02-19T09:55:45.000Z","published_at":"2020-11-07T11:28:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 44\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 45\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 49\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 51\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 56\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(9) = 56\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(10) = 57\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47405,"title":"Find Logic 31","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.476px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 155.738px; transform-origin: 174px 155.738px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 23\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 19\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 31\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 41\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(7) = -1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(8) = 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 21;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 23;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 19;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 31;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 41;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = -1;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":195,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T11:49:35.000Z","updated_at":"2026-02-14T13:50:16.000Z","published_at":"2020-11-07T11:49:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 19\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 31\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(7) = -1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(8) = 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44449,"title":"Moving Median Absolute Deviation","description":"The median absolute deviation (MAD) is defined as\r\nMAD = median(abs(A − median(A)))\r\nfor a rolling window of length n. For example:\r\nmove_mad(1:10, 5) \r\nreturns [1 1 1 1 1 1];\r\n\r\nmove_mad(logspace(0, 1, 10), 3) \r\nreturns [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]\r\nRound the result to 3 digits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.8px; transform-origin: 407px 112.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe median absolute deviation (MAD) is defined as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 128px 8.5px; transform-origin: 128px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 76px 8.5px; transform-origin: 76px 8.5px; \"\u003eMAD = median(abs(A \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(255, 0, 0); border-block-start-color: rgb(255, 0, 0); border-bottom-color: rgb(255, 0, 0); border-inline-end-color: rgb(255, 0, 0); border-inline-start-color: rgb(255, 0, 0); border-left-color: rgb(255, 0, 0); border-right-color: rgb(255, 0, 0); border-top-color: rgb(255, 0, 0); caret-color: rgb(255, 0, 0); color: rgb(255, 0, 0); column-rule-color: rgb(255, 0, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(255, 0, 0); perspective-origin: 8px 8.5px; text-decoration: none; text-decoration-color: rgb(255, 0, 0); text-emphasis-color: rgb(255, 0, 0); transform-origin: 8px 8.5px; \"\u003e− \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; \"\u003emedian(A)))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a rolling window of length n. For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emove_mad(1:10, 5) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003ereturns \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 52px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 52px 8.5px; \"\u003e[1 1 1 1 1 1]\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 128px 8.5px; transform-origin: 128px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emove_mad(logspace(0, 1, 10), 3) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 228px 8.5px; transform-origin: 228px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003ereturns \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 196px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 196px 8.5px; \"\u003e[0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRound the result to 3 digits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function stats = move_mad(v, n)\r\n    \r\nend","test_suite":"%%\r\nv = 1:10;\r\nn = 5;\r\nstats_correct = [1 1 1 1 1 1];\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);\r\n\r\n%%\r\nv = logspace(0, 1, 10);\r\nn = 3;\r\nstats_correct = [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748];\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);\r\n\r\n%%\r\nrng('default');\r\nv = randn(1000, 1);\r\nn = 990;\r\nstats_correct = 0.660 * ones(1, 11);\r\nstats = move_mad(v, n);\r\nassert(sum(abs(stats - stats_correct)) \u003c 1e-3);","published":true,"deleted":false,"likes_count":0,"comments_count":6,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2021-07-03T05:49:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-12T08:08:02.000Z","updated_at":"2025-11-18T17:43:42.000Z","published_at":"2017-12-12T08:08:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe median absolute deviation (MAD) is defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[MAD = median(abs(A − median(A)))]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor a rolling window of length n. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[move_mad(1:10, 5) \\nreturns [1 1 1 1 1 1];\\n\\nmove_mad(logspace(0, 1, 10), 3) \\nreturns [0.292 0.377 0.486 0.628 0.811 1.048 1.353 1.748]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRound the result to 3 digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57646,"title":"Easy Sequences 93: Recursive Polynomial Function","description":"For a natural number  and a polynomial function , we define a recursive function , as follows:\r\n                ,  and\r\n                ,  for .\r\nFor example, if  (or in Matlab array form, P = [1 2 1]):\r\n                \r\n                \r\n                \r\n                \r\n                ...\r\n                \r\n                and so on...\r\nWe can see that  can grow very quickly. Therefore, we will instead calculate: , that is, is equal to the logarithm (base-) of the absolute value of .\r\nGiven a polynomial array , and an integer , find the value of , rounded-off to 4 decimal places.\r\n----------------------\r\nNOTE: To encourage vectorization , FOR and WHILE loops are disabled. If you know the math, this problem can be solved in less than 15 lines of code. However, solutions up to 50 lines of code will still be accepted. The semicolon (;), shall be considered as an end-of-line character. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 505px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 252.5px; transform-origin: 407px 252.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31.5px; height: 18.5px;\" width=\"31.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define a recursive function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 18.5px;\" width=\"79\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 167.5px; height: 18.5px;\" width=\"167.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 118.5px; height: 19.5px;\" width=\"118.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or in Matlab array form, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44px 8px; transform-origin: 44px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; \"\u003eP = [1 2 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 318.5px; height: 19.5px;\" width=\"318.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan 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taBiWg7IsA7cDmt5FmHIWyu2SD3Uuo2tOK/Ht9U3ejE2m29Umz26N3MavbdtZdXpmW2rrTI87bfW0ZsugjDqcTo7aZb1PzRh5GQ5sjDxYq/TrySMEXZupm2ed+kksIY09PI+JcLYC1XqtZV/94Yqlfny/EDEwq/Zny3CaPmah+d0LMnlrGeHA9ViIGgYI4C0dv7qdBxQUQPUWl/rJ+qsXmf2jbUdGJw4Nde6uBx53izS8iZj2xwDzHNQpodR9JZ0Oa5mt9qixp5H91imZ0HQw/nYf/e0f1VdZwmjPj0deR0K23towsjF0KG/frWKMEbZuVX6p/O1fm3HU5dTIoyedq1Kq+flWVvb7c8WYdRbYi1vlj4d2/KEcBJskTd96m3rQlDer4VgWEv8GpTvWpHyI9yrOm82X5J03mWIeCf9HGs1jTqUMXU14u/xOoNcWk45s93whiBgf+u5VH6Jk5+trw/QyEfGL6Iu0YRRHyBqfQ7Qqm+WsRete/TOj8SoWtsVmS66/ZF103nNEEZ9ahpjqfWVlNH6RxJGzkG1jxVEe7c8bV5BGKPsnKcdrbQ8ALF1OTq/toMY2EiynoTR13vUGcuO43R/1ghjefFp665Fz+nb3iRSelZAnHDdw70il4nAu3S9SEmkahBbCYmvi9al1liiFBjKm86Kw2EVrCA+JDJyYGWm1jQO+sLW2mqm7MOWB9FC6EtMWu3onf7GBAMdGvlMZKvcSMJY3p8HHYj4HGRv7EXqnoWgzujjincj27+ifsgTuGKBxWtyPIcIOdaQj+dLWd62RBJGHRONeoC44NQxHnxRCmPjOpGZQ0Te9jF9NGGMtHOjbSrf07tF+Bvm4gsiWJzjOiYsOiLuddTlriaMesEVZVuj8B7Jhw47iy2Y7s8twghAcblz+eCy2R+KoILlo2P9cGXCnZV0HGQt1ynS4PJOGEc8vAbibvnZQ5SQz10iljjHkY5a9Q4Mx1UivKAZuF8QgbE8hmEs68N2s1+2viVaXr1Ru1qCLnBsD2/pFXQAk4b1+ZUkrN0xxrKuduqRpewowtjCujamLPVDGsvYi9I92BBM6CMHzaztWZEuqv3RdcM4wBU4+OpV+fDy9nIRDX2/QgSfb4XnHbsyd4jgOp3adTcR9Y4kjGgDPkX3UlUxjPF7RHpfkopoSyuPSMIYaeci272ld7DlxH+FHq0ijDXbCrzQpmPNr7P9Re5liYOc7s/eoZfZxmy9TzKxeqsK7teviUR/HH0FJuc5T2wFfklkddjASr2DMXqkyE9EZr9gsVIXVmLAejOsBF+/2DMWK3HeQ97ohytFficye22Hpz2Y8PGAmM580cZT5jHSAl+QWTw5x8T1AIj400VASrecCHElZU5uBI5BGLm9ecNChaCXdDUpdQOeL2wiQC9i5EEUXRC9zatJ6d679xBjDyve2cuK945j1i8RSAQSgXOHwDEII0BmnFZksCw7D+TgRpHe963PXWfvvMEgGrcsWESs1LWdQ7pZvZV4YKF2mcgq4n+KeGedE4FEIBG4KBA4FmEkabxNfkCwZlRsHu9vs5ygvig68CJrBDyNtTjZkaaCHEXr2Eg99vbOClywLY/PzyVZ3FtvZ30SgUQgEQhA4JiEkaTxcvkhKtYJ8XCegzEBEGYWwQhE9mHvEu/gqp9Udvz8Xo69k+q2rGwikAgkAsdB4NiE8TitzlITgUQgEUgEEoFEIBFIBMwIJGE0Q5UJE4FEIBFIBBKBRCAROJ8IJGE8n/2erU4EEoFEIBFIBBKBRMCMQBJGM1SZMBFIBBKBRCARSAQSgfOJQBLG89nv2epEIBFIBBKBRCARSATMCPwP6NoYgjQFVzQAAAAASUVORK5CYII=\" style=\"width: 326px; height: 19.5px;\" width=\"326\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 118px; height: 18.5px;\" width=\"118\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                and so on...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe can see that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can grow very quickly. Therefore, we will instead calculate:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 108.5px; height: 18.5px;\" width=\"108.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAlCAYAAADyUO83AAAD1ElEQVRoQ+2ZO69OQRSGv/MDxLXTiEshIcS1QaFASDQiiEbnUihIiFtJQqJRuCRawQ8gKDQ0LgW1S0GicvkJvM/JXslkzJo98+3Nzsn5Jln59pnLWjPvvGutmTlTo1lepmb5+kcTACYMGBaBNTK/WPK4p2kclZ47NbqGdAEWf1VyWPKjZtKZvrvVdrJGZw6ALR0n9U3jPzs6WPxdya4eF2+mDurjdKluDwAm+C6Y/C99v27+Xq7fZUHbU6eePikAFqr+g2Sv5GVHkL3hZ9SwRHKiTb8HAL50W/JQcj5ayBP9vbNRfEW/FwIjoH9f8lay0THOeIBpnVzb5DPtgPxKgjtk44sHwAMNnCeBomFB8fegYk/CwBvVPYuAsSG41QuJx44Oa/5rKJtxU7JC4sYYD4DfGrQoMZAg8ygwlRrPDt9wkP8fu2/TM1c7pwo3M6QWsFQDNklgQVwuqwKXoOD7MUOop0/oFqbD4kqKNX3ufKgLBuyQELeSpTYNQu8Njaaz+r1WMXMDL8WsCjVVXS0mrdWo96mRNQDE/u8qdaYIeBQvOHorw+5KSSqtwqo5Ei+bGOuOqU/SDWoACP2ftLigai9GI+KK5zaxKhZ9qqGvMY6xdmii/Z7EslHOrbB7S5LMOjUA4E/Hm5mSHqFXabGdKHUbFjhXQroM7RrrYNMnCZkKEHJszAJfA8BHGbIDkEspBxFLf6UAhGpsLHWHJKsl870dTdgn8xAEk4GwFAAyA4hbqc3jXQDAJrtI4YBFqYkjdnBLrrUUAIumGAcIN638AwagMjx91gbfXgAI/dANKM7iqe7KAM723BwptWk0m31KGfBThvE7yjgHGXOhcWIANu1uwvdWSc0lqnMQjG+GtTtgxKhJgyGZYvvxBSxDvOkm7LpjShgQol+ax1OTykZjZxV2q7uo9iMSUl7uphmrMdcje6SO9kWPogw80Ggel8IhjWsYhG2CLneLVBxgc75KvCuvbZ6btdoYUHL9baOgtVsccHdDHTltrpLANCbPGLtwxecB9PLyk0uJsI6SurRNN7QBEEZ/+ucmXwJE24Qs36OLnd8sCe/yYTBOtYdzKAHcBQC6rZNw1IzLc1V8kSR9qgWFtgcR7G6XcAS+FC0e1fbo6bWH5tG1X5I9NLUxoGRXa/twLV4vcWlZqzDRn90nWLa+Ow4BAHEFV7g+JotK8EE/TG19rxgCABZg6W2fvpMPFSWrdPoUvwgzfigADATu9KTWvkDgzrJNUvziPCQABgKvPTVH2xw5CJJV/2YbGoAOTO9n6ASAfnCcuVomDJi5e9fPzP8AmsXMJndcxcwAAAAASUVORK5CYII=\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis equal to the logarithm (base-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the absolute value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a polynomial array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, rounded-off to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55px 8px; transform-origin: 55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e----------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization , \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFOR and WHILE loops are disabled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If you know the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003emath\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, this problem can be solved in less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e15\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lines of code. However, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esolutions up to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003e50\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e lines of code will still be accepted\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52px 8px; transform-origin: 52px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The semicolon (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159px 8px; transform-origin: 159px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), shall be considered as an end-of-line character. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = T(P,x)\r\n    t = round(log(abs(R(x))),4);\r\n    function r = R(x)\r\n        if x == 0\r\n            r = polyval(P,x);\r\n        else\r\n            r = x * R(x-1) + polyval(P,x);\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nP = [1 2 1]; x = 0:10;\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [0.0000 1.6094 2.9444 4.2905 5.7589 7.3908 9.1876 11.1344 13.2140 15.4113 17.7139];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [1 0 1]; x = [10 100 1000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [17.2030 365.8380 5914.2268];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [-1 1 -1 1]; x = [10 100 1000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [17.2030 365.8380 5914.2268];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [1 2 3 4 5]; x = [10 100 1000 10000];\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [19.7933 368.4283 5916.8171 82113.6167];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = [11 -22 33 -44 55 -66]; x = 12345;\r\nt = T(P,x);\r\nt_correct = 103969.6836;\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = 2:2:10; x = P.*200;\r\nt = arrayfun(@(i) T(P,i),x);\r\nt_correct = [2005.8827 4557.3328 7317.9383 10214.4041 13211.9064];\r\nassert(isequal(t,t_correct))\r\n%%\r\nP = 2:2:100; x = P./2;\r\nt = arrayfun(@(i) T(P,i),x);\r\ns = round([mean(t) median(t) mode(t) std(t)],4);\r\ns_correct = [163.8877 167.4357 7.8823 59.1051];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('T.m');\r\nnot_allowed = contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'java') || contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)\r\nassert(count(filetext, 'function')==1)\r\n\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=50)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-14T06:56:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2023-02-07T04:59:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-03T04:56:19.000Z","updated_at":"2025-11-26T02:41:15.000Z","published_at":"2023-02-06T08:01:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we define a recursive function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(0)=P(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x) = x\\\\cdot R(x-1) + P(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x) = x^2+2x+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or in Matlab array form, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP = [1 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(0) = P(0)=0^2+2\\\\cdot 0 + 1=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(1) = 1\\\\cdot R(0)+P(1)=1\\\\cdot 1+1^2+2\\\\cdot 1 + 1=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(2) = 2\\\\cdot R(1)+P(2)=2\\\\cdot 5+2^2+2\\\\cdot 2 + 1=19\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(3) = 3\\\\cdot R(2)+P(3)=3\\\\cdot 19+3^2+2\\\\cdot 3 + 1=73\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(10) = 49320491\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                and so on...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can see that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can grow very quickly. Therefore, we will instead calculate:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x) = \\\\text{log}|R(x)|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis equal to the logarithm (base-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the absolute value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a polynomial array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, rounded-off to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e----------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization , \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFOR and WHILE loops are disabled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If you know the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emath\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, this problem can be solved in less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e15\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lines of code. However, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esolutions up to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e50\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e lines of code will still be accepted\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The semicolon (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), shall be considered as an end-of-line character. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47390,"title":"Find Logic 29","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 371.381px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 185.69px; transform-origin: 174px 185.69px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,1) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,2) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,3) = 40\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1,4) = 85\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,2) = 32\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2,3) = 65\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3,3) = 108\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,2) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4,3) = 175\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5,1) = 156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(a,b) which will return value according to problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(a,b)\r\n  y = 4;\r\nend","test_suite":"%%\r\na = 1;\r\nb = 1;\r\ny_correct = 4;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ny_correct = 15;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ny_correct = 65;\r\nassert(isequal(logic(a,b),y_correct))\r\n\r\n%%\r\na = 4;\r\nb = 2;\r\ny_correct = 120;\r\nassert(isequal(logic(a,b),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-07T02:37:38.000Z","updated_at":"2026-02-25T13:59:58.000Z","published_at":"2020-11-07T02:37:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,1) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,2) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,3) = 40\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1,4) = 85\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,2) = 32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2,3) = 65\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3,3) = 108\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,2) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4,3) = 175\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5,1) = 156\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(a,b) which will return value according to problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53725,"title":"Easy Sequences 56: Counting \"Ugly\" Numbers","description":"A positive integer  is called a regular number, if and only if there exist a non-negative integer , such that .  For some reason, such a number is also refered to as an ugly number. Below are the first few regular numbers:\r\n                            \r\nIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only  regular numbers  and just  regular numbers .\r\nGiven an integer , and exponent , we are tasked to write a function that counts the number of regular numbers less than or equal to .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 174px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA positive integer\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Regular_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is called a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Regular_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eregular number, \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eif and only if there exist a non-negative integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"20\" style=\"width: 49px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.  For some reason, such a number is also refered to as an \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eugly number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Below are the first few regular numbers:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"515.5\" height=\"19\" style=\"width: 515.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e regular numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"19\" style=\"width: 42.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and just \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47\" height=\"18\" style=\"width: 47px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e regular numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"19\" style=\"width: 40px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, we are tasked to write a function that counts the number of regular numbers less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = regCount(n,e)\r\n    c = n ^ e;\r\nend","test_suite":"%%\r\nn = 10; e = 5;\r\nc_correct = 313;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 10; e = 10;\r\nc_correct = 2053;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 2; e = 100;\r\nc_correct = 48694;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 7; e = 77;\r\nc_correct = 473183;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 10; e = 100;\r\nc_correct = 1697191;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\nn = 77; e = 77;\r\nc_correct = 5166439;\r\nassert(isequal(regCount(n,e),c_correct))\r\n%%\r\n%ns = 1:100; es = ns+10;\r\n%cs = arrayfun(@(i) regCount(ns(i),es(i)),1:100);\r\n%ss = floor([cs(25:25:end) sum(cs) std(cs) sum(num2str(cs))]);\r\n%ss_correct = [203379 1797050 6815143 17856016 421336320 5052973 44715];\r\n%assert(isequal(ss,ss_correct))\r\n%%\r\nns = 1:25; e = 100;\r\ncs = arrayfun(@(i) regCount(ns(i),e),1:25);\r\nss = floor([cs(5:10:end) sum(cs) std(cs) sum(num2str(cs))])\r\nss_correct = [585064 2751849 4607635 57125382 1487797 10278];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('regCount.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":27,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2021-12-19T18:30:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-17T16:20:39.000Z","updated_at":"2026-03-19T15:29:37.000Z","published_at":"2021-12-17T17:33:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Regular_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is called a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Regular_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eregular number, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003eif and only if there exist a non-negative integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\\\\ |\\\\ 60^k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.  For some reason, such a number is also refered to as an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eugly number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Below are the first few regular numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60...\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt turns out that regular numbers are not so regular after all. In fact, regular numbers are quite rare. There are only \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2,053\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e regular numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le10^{10}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and just \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e48,694\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e regular numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le2^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are tasked to write a function that counts the number of regular numbers less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53755,"title":"Easy Sequence 61: Wide Pythagorean Triangles","description":"An integer-sided right triangle with sides , is called a \"wide Pythagorean triangle\", if , and . \r\nWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit .\r\nBelow is the list of all Pythagorean triangles with all sides :\r\n    \r\nTherefore, for , your program output should be . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111.25px; transform-origin: 407px 111.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128px 8px; transform-origin: 128px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn integer-sided right triangle with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 47.5px; height: 18.5px;\" width=\"47.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is called a \"wide Pythagorean triangle\", if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAkCAYAAABG3S5jAAADBUlEQVR4nO2aa5GsMBCFjwccYAADowAFOMDBOsACGpCAByyg4VrY+yN0cWAJhKTDTO32V5XaF5tHn0660wxgGIZhGIZhGMb7KQC8ALTLV+MzeC2t0uhoBPBNzYR+LwWAHltNvgH8g9uISbDYGtQASqW+/hIlnKB7kbl1KQNMSydj0jRXxHE6mOB3GAHMABr6XYWfO7yO6bykDpKPhoUWW8/8rYKLQ2vYrYazmS8ef2G15xAzQEMdJAd9ooCb3G8WXFPo4aKfAtt4HTVA9D8HcCR4D12neheaQve43gQyXpRWIkBPv5Pr1mv5XoMjwUfkF7yEWwcbsVIaV1PoO+PdzqUqrEZvcJzaq6T1xFOCN3CJzbSMN8CFDhlXY01PCz3HjscBvoQzygC3AxpsxdAWIpfgBfwCyO1Caz1PCi1J84yIPIevVRN+TpgTta+kafoRwfkUGREXMgqsazoyvggzR83U398TQouNbo+1z+KOLuIveibpon6CHLEyzoTtPTIUFrn3PHP19z0S331N+usunkvNcwo4jaLqHLxbfR5e0zPaXrsXeECcwEJHfR0Zlh07tOCwP2liW2qYGOCcKsphOOnyLZyNpxWjjwROra9z0cd38rBjhxqsgdtFvib5xXzxXErtoF36j7Y/T9KHCKJRGs0hsMBO6zOqjD0pjQnkj9Fis2iR+VrlmyTvgBRBcgosiNP6RMyVVOYUOllkwE3sbAdI8E8xzF7gDnmKI+y0R8c2r+VOfA4hl9A1rkWuEBASrq4Z8veo4jnWsuoT9e2zm4Fk4jyfAusboVRyCF3BOebZqSfrOrUrZ5/7o44rYymGGPHcCwxeD9+/pQDUYl3ThNWQn1gwkblJNc/XJPk7hV9uc8oux8WVN4Xw9BsqTsbECFLWBf0sNQOtEKIptIgcemULCkEFnBEGrFeALvSfP5QW61pabK9Q8pEp7VNG+zXl2RWN2wC9l01JVDivFIW0j1jIBQ3cUfpnP2e3/8DhO6pJxgN0CD+GclSTDMMwDMMwDMMwMvAfreWdn1Mz1fQAAAAASUVORK5CYII=\" style=\"width: 61px; height: 18px;\" width=\"61\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 60px; height: 18px;\" width=\"60\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003es\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 102.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 51.25px; text-align: left; transform-origin: 384px 51.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-45px\"\u003e\u003cimg 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\" style=\"width: 745px; height: 102.5px;\" width=\"745\" height=\"102.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 50px; height: 18px;\" width=\"50\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, your program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = countWPTs(s)\r\n    c = length(primes(s)) + 20;\r\nend","test_suite":"%%\r\ns = 100;\r\nc_correct = 45;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 300;\r\nc_correct = 196;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000;\r\nc_correct = 857;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000;\r\nc_correct = 12397;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000;\r\nc_correct = 161208;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 1000000;\r\nc_correct = 1979930;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 10000000;\r\nc_correct = 23469232;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\ns = 100000000;\r\nc_correct = 271353574;\r\nassert(isequal(countWPTs(s),c_correct))\r\n%%\r\nss = floor((pi/2) .^ (11:40));\r\ncs = arrayfun(@(s) countWPTs(s),ss);\r\nss = [sum(cs) nnz(find(cs)) floor(std(ss)) sum(num2str(cs))];\r\nss_correct = [487155754 30 15528091 13675];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('countWPTs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-05T05:25:43.000Z","updated_at":"2025-11-21T18:31:53.000Z","published_at":"2022-01-05T08:26:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn integer-sided right triangle with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[a,b,c]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is called a \\\"wide Pythagorean triangle\\\", if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb \\\\ge a+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec \\\\ge b+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a program that counts all wide Pythagorean triangles whose no sides greater than a given limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBelow is the list of all Pythagorean triangles with all sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ \\\\ [6,8,10],\\\\ [9,12,15],\\\\ [8,15,17],\\\\ [12,16,20],\\\\ [15,20,25],\\\\ [10,24,26],\\\\ [18,24,30],\\\\ [16,30,34],\\\\ [21,28,35],\\\\ \\\\\\\\\\n\\\\ \\\\ [12,35,37],\\\\ [15,36,39],\\\\ [24,32,40],\\\\ [27,36,45],\\\\ [30,40,50],\\\\ [14,48,50],\\\\ [24,45,51],\\\\ [20,48,52],\\\\ [28,45,53],\\\\ \\\\\\\\\\n\\\\ \\\\ [33,44,55],\\\\ [40,42,58],\\\\ [36,48,60],\\\\ [39,52,65],\\\\ [25,60,65],\\\\ [16,63,65],\\\\ [33,56,65],\\\\ [32,60,68],\\\\ [42,56,70],\\\\ \\\\\\\\\\n\\\\ \\\\ [48,55,73],\\\\ [24,70,74],\\\\ [45,60,75],\\\\ [21,72,75],\\\\ [30,72,78],\\\\ [48,64,80],\\\\ [18,80,82],\\\\ [51,68,85],\\\\ [40,75,85],\\\\ \\\\\\\\\\n\\\\ \\\\ [36,77,85],\\\\ [60,63,87],\\\\ [39,80,89],\\\\ [54,72,90],\\\\ [35,84,91],\\\\ [57,76,95],\\\\ [62,72,97],\\\\ [60,80,100],\\\\ [28,96,100]\\\\ \\\\}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, your program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e45\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53109,"title":"Easy Sequences 52: Non-squarable Rectangles ","description":"Any integer-sided rectangle can be cut into unit rectangles () and rearranged into sets of smaller rectangles. For example the  rectangle can be broken as follows:\r\n                                                      \r\nWe call an integer rectangle as \"squarable\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of non-unit squares of equal sizes. For example the  rectangle can be broken into six  squares. Therefore, the  rectangle is squarable.\r\n                                                \r\nInteger rectangles that are not squarable are called \"non-squarable\". The  rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area  square units are as follows:\r\n\r\nCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit . \r\nFor , the program should output:\r\n        \r\nNOTE: Reflections and rotations are not significant and should be counted only once.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 544px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 272px; transform-origin: 407px 272px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.5px 8px; transform-origin: 188.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAny integer-sided rectangle can be cut into unit rectangles (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAkCAYAAADfJffWAAABK0lEQVRoge2YUQ2DMBBAnwcc1AA+UFAHc1AHWEDDJMzDLEzDLGwfhaxkhNBysN5yL2n4uvZ4NL0rYBiGYRi144Dm10nsoJWczAED8JKe+CQ88ACuEpM1fGRMQ5OUjihjyn23lA4I4/OOPik9cBmHmJSUgD4pKdVKaYEncefl4Mc4V7guVCwlPZu2ivFJTF+4LlQsBfLESAmByqXANjGSQkCBFFgXIy0ElEiBZTFHCAFFUmAupucYIaBMCnx3zNJCQKGUtOPMKdc5qJKSniHpHUVajBopS4dqSYO3BRVS1qrMEWKql7Kl7EqLqVpKTh8iKUZcimN+CIbCeUoaMwkx6Qd9sO+2jSMmf1sYA7GU5jC9YG4fUhrniTtjKf9ARf+F/MlxhmEYhmEYf8Ub9AbIMJOfOosAAAAASUVORK5CYII=\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167px 8px; transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and rearranged into sets of smaller rectangles. For example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.5px 8px; transform-origin: 113.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle can be broken as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 80.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 40.25px; text-align: left; transform-origin: 384px 40.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                      \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 246px;height: 75px\" 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bj45ODQ8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KO1Qc/QAAABxpRE9UAAAAAgAAAAAAAACWAAAAKAAAAJYAAACWAAAVm4ZFF1QAABVnSURBVHgB7N1BdiXF0QZQyUtohniGd4A99toZAzswMxjCEpCxdSIHnH7odFGNIuK7nlT90E+uuJGZld/Llv/nl9/+8+Q/BAgQIECAAAECBAgQIECAwJ8SeBaw/5SfDxMgQIAAAQIECBAgQIAAgf8LCNgGAgECBAgQIECAAAECBAgQuEFAwL4B0Y8gQIAAAQIECBAgQIAAAQICtjFAgAABAgQIECBAgAABAgRuEBCwb0D0IwgQIECAAAECBAgQIECAgIBtDBAgQIAAAQIECBAgQIAAgRsEBOwbEP0IAgQIECBAgAABAgQIECAgYBsDBAgQIECAAAECBAgQIEDgBgEB+wZEP4IAAQIECBAgQIAAAQIECAjYxgABAgQIECBAgAABAgQIELhBQMC+AdGPIECAAAECBAgQIECAAAECArYxQIAAAQIECBAgQIAAAQIEbhAQsG9A9CMIECBAgAABAgQIECBAgICAbQwQIECAAAECBAgQIECAAIEbBATsGxD9CAIECBAgQIAAAQIECBAgIGAbAwQIECBAgAABAgQIECBA4AYBAfsGRD+CAAECBAgQIECAAAECBAgI2MYAAQIECBAgQIAAAQIECBC4QUDAvgHRjyBAgAABAgQIECBAgAABAgK2MUCAAAECBAgQIECAAAECBG4QELBvQPQjCBAgQIAAAQIECBAgQICAgG0MECBAgAABAgQIECBAgACBGwQE7BsQ/QgCBAgQIECAAAECBAgQICBgGwMECBAgQIAAAQIECBAgQOAGAQH7BkQ/ggABAgQIECBAgAABAgQICNjGAAECBAgQIECAAAECBAgQuEFAwL4B0Y8gQIAAAQIECBAgQIAAAQICtjFAgAABAgQIECBAgAABAgRuEBCwb0D0IwgQIECAAAECBAgQIECAgIBtDBAgQIAAAQIECBAgQIAAgRsEBOwbEP0IAgQIECBAgAABAgQIECAgYBsDBAgQIECAAAECBAgQIEDgBgEB+wZEP4IAAQIECBAgQIAAAQIECAjYxgABAgQIECBAgAABAgQIELhBQMC+AdGPIECAAAECBAgQIECAAAECArYxQIAAAQIECDz98s9/UAgU+PDdf1ZWbTy/tnVrf1cOWkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KaAQPIm0co/sDWAGc+vw3Vrf1dORkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KaAQPIm0co/sDWAGc+vw3Vrf1dORkWtERCw17RSIQQIECBA4LqAQHLdbvIntwYw4/l1VG7t7+Q559n3CwjY+3usQgIECBAg8KbAo0Dy4dtv3vzs5D/w/Le/P728vDw9vfw0uYw3n/2Xf/37o39mawBLG89p/f3oYPYPCTQRELCbNMJjECBAgACB9xRICyTH+vnLp+fn56eXX388/2jjTVoASxvPaf3dOEfVtEdAwN7TS5UQIECAAIHLAmmBpKCcYGf9/8He+jcyBOya0a4E3l9AwH7/HngCAgQIECDw7gKpAfvJCfa7j73P8QBp41nA/hyjyM8kcE1AwL7m5lMECBAgQGCVQFogqeY5wXaCXWNh8lXAntw9z75NQMDe1lH1ECBAgACBCwKpAdsJtoB9Ybq0+4iA3a4lHihYQMAObr7SCRAgQIBACaQGbCfYAnbNgclXAXty9zz7NgEBe1tH1UOAAAECBC4IpAZsJ9gC9oXp0u4jAna7lnigYAEBO7j5SidAgAABAiWQGrCdYAvYNQcmXwXsyd3z7NsEBOxtHVUPAQIECBC4IJAasJ1gC9gXpku7jwjY7VrigYIFBOzg5iudAAECBAiUQGrAdoItYNccmHwVsCd3z7NvExCwt3VUPQQIECBA4IJAasB2gi1gX5gu7T4iYLdriQcKFhCwg5uvdAIECBAgUAKpAdsJtoBdc2DyVcCe3D3Pvk1AwN7WUfUQIECAAIELAqkB2wm2gH1hurT7iIDdriUeKFhAwA5uvtIJECBAgEAJpAZsJ9gCds2ByVcBe3L3PPs2AQF7W0fVQ4AAAQIELgikBmwn2AL2henS7iMCdruWeKBgAQE7uPlKJ0CAAAECJZAasJ1gC9g1ByZfBezJ3fPs2wQE7G0dVQ8BAgQIELggkBqwnWAL2BemS7uPCNjtWuKBggUE7ODmK50AAQIECJRAasB2gi1g1xyYfBWwJ3fPs28TELC3dVQ9BAgQIEDggkBqwHaCLWBfmC7tPiJgt2uJBwoWELCDm690AgQIECBQAqkB2wm2gF1zYPJVwJ7cPc++TUDA3tZR9RAgQIAAgQsCqQHbCbaAfWG6tPuIgN2uJR4oWEDADm6+0gkQIECAQAmkBmwn2AJ2zYHJVwF7cvc8+zYBAXtbR9VDgAABAgQuCKQGbCfYAvaF6dLuIwJ2u5Z4oGABATu4+UonQIAAAQIlkBqwnWAL2DUHJl8F7Mnd8+zbBATsbR1VDwECBAgQuCCQGrCdYAvYF6ZLu48I2O1a4oGCBQTs4OYrnQABAgQIlEBqwHaCLWDXHJh8FbAnd8+zbxMQsLd1VD0ECBAgQOCCQGrAdoItYF+YLu0+ImC3a4kHChYQsIObr3QCBAgQIFACqQHbCbaAXXNg8lXAntw9z75NQMDe1lH1ECBAgACBCwKpAdsJtoB9Ybq0+4iA3a4lHihYQMAObr7SCRAgQIBACaQGbCfYAnbNgclXAXty9zz7NgEBe1tH1UOAAAECBC4IpAZsJ9gC9oXp0u4jAna7lnigYAEBO7j5SidAgAABAiWQGrCdYAvYNQcmXwXsyd3z7NsEBOxtHVUPAQIECBC4IJAasJ1gC9gXpku7jwjY7VrigYIFBOzg5iudAAECBAiUQGrAdoItYNccmHwVsCd3z7NvExCwt3VUPQQIECBA4IJAasB2gi1gX5gu7T4iYLdriQcKFhCwg5uvdAIECBAgUAKpAdsJtoBdc2DyVcCe3D3Pvk1AwN7WUfUQIECAAIELAqkB2wm2gH1hurT7iIDdriUeKFhAwA5uvtIJECBAgEAJpAZsJ9gCds2ByVcBe3L3PPs2AQF7W0fVQ4AAAQIELgikBmwn2AL2henS7iMCdruWeKBgAQE7uPlKJ0CAAAECJZAasJ1gC9g1ByZfBezJ3fPs2wQE7G0dVQ8BAgQIELggkBqwnWAL2BemS7uPCNjtWuKBggUE7ODmK50AAQIECJRAasB2gi1g1xyYfBWwJ3fPs28TELC3dVQ9BAgQIEDggkBqwHaCLWBfmC7tPiJgt2uJBwoWELCDm690AgQIECBQAqkB2wm2gF1zYPJVwJ7cPc++TUDA3tZR9RAgQIAAgQsCqQHbCbaAfWG6tPuIgN2uJR4oWEDADm6+0gkQIECAQAmkBmwn2AJ2zYHJVwF7cvc8+zYBAXtbR9VDgAABAgQuCKQGbCfYAvaF6dLuIwJ2u5Z4oGCBdgH70Qs+uEdKJ0BgmMCH73ZuWIe1weN+osCj9++Hb7/5xJ806487wd65XqWN57SA/ai/s1YfT/upAlP2VwL2p3bWnydAgMAbAlNeAG+U4V+HCTzasG4P2E6wBewNU13A3tBFNbwlMGV/JWC/1Un/ngABAp8oMOUF8Ill+ePLBR4F7C++/+Hp5eXl6fn52XWww6P+bl2vHtW7dTw/qjetv8uX6fjypoxnATt+qAIgQOBugSkvgLvr9vNmC/zRBl24nv/lws9ff/XRAbp1vUobz/r70eHtHy4TmLJeCdjLBp5yCBB4f4EpL4D3l/IEnQQeBhK/g92pTZefxV8hfqXb+isP+nt5avjgIIEp+ysBe9Cg8qgECMwQmPICmKHpKf8qgdSA7Xew/Q72XzXHPud/j4D9OXX97C4CU/ZXYwL21m8ca8Cm/K+YqvenIlh9TRnPaRua1YNWcU+pAdt6JWBvmP5p7yPr1e795PTxLGB3WVWfv3z9H5D59ccuT/R5n0O9n9f3vX96SH+nvwDee5j47+8lkLphdYItYPeaideeJu19ZL3anRemj2cB+9o6dvunUr5BLzj1lsTOa0p/p78Ado4+VV0VSN2wWq8E7KtzptPn0t5H1isn2J3m3++fRcD+vch7/d8hJ36HV72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVQOqG1XolYNccmHxNex9Zr5xgd56vAnaX7oSc+B1u9R6KlTch/U3b0Kwcq4o6AqkbVifYAvaZBINv0t5H1isn2J2nq4DdpDsp36AXt3pLYuc1pb9pG5qdo1VVJZC6YbVeCdg1ByZf095H1isn2J3nq4DdpTshJ36HW72HYuVNSH/TNjQrx6qijkDqhtUJtoB9JsHgm7T3kfXKCXbn6SpgN+lOyjfoxa3ekth5Telv2oZm52hVVQmkblitVwJ2zYHJ17T3kfXKCXbn+Spgd+lOyInf4VbvoVh5E9LftA3NyrGqqCOQumF1gi1gn0kw+CbtfWS9coLdeboK2E26k/INenGrtyR2XlP6m7ah2TlaVVUCqRtW65WAXXNg8jXtfWS9coLdeb4K2F26E3Lid7jVeyhW3oT0N21Ds3KsKuoIpG5YnWAL2GcSDL5Jex9Zr5xgd56uAnaT7qR8g17c6i2JndeU/qZtaHaOVlWVwKMNa/17150CH77LCtg7u/i4qrT+fvj2m8cYC/6N/dWM9UrA7jLZQk78Drd6D8XKm5D+CtgrR29sUQJ2ZuvTAlhal9P6uz1g+xs3AvalNezRC/6L7394enl5eXp+fnblYByYBy3WgUfr1dYNzaVF3YfGCDwaz2MK8KCXBLauV8bz63BI66+8sCMnPZq/U8bznBPs3/4Kk3C9Y9Looz5u+bLs56+/+uiGdsoL4KMP7x/GCjza0MSChBS+db0ynl8HcFp//1evfeb8feb0/dWcgO13Kla96lN+h6Sapt6S2HX1V8R39TO9GoEkcwSkBbC0Lqf1d/tfEU/ZT07fXwnYXVbakN9ZPdzqPRQrb0L6O/0FsHLsKeqygIB9mW70B9MC2OhmXXj4tP5uD9h+B3vG72D/FwAA//8vMK6DAAAX/0lEQVTt3bF2JUmRxvEW3ri9JnjwBoC9T7MHbx4Gj8PTjD3DG4AH5uKOt70jdCKPUOkOXXXrqjLj+7WTqWpV3Yp/RGTGlyF1P3356c+nif7883e/efdtPn//3bvXu1x8+sWvPv3LFV/+0cWkn7WDvT+LZ/m/TPHvP3//3+/66vMPf333uosIIIAAAgggcD8BeqG3Xli9vnoisO9P8lOe8PTLT09PT5++/N/fT3nc9A9h7/QuuusFQ/y7+gZwl4/djAACCCCAwEUEUgX2J/XVRRG372MJ7H28HvbdKR2/AsjeItFzTPEvgd0zflmFAAIIIDA3gVSBrb5a4ycECexZ1o+QE6mBm70DRctJiH8J7JbRyygEEEAAgckJpApsHWwC+1BqpiZMyolUBQV7i0TPMcW/BHbP+GUVAggggMDcBOgFv4M9c4TqYM/inZCO38DN3oGi5STEvwR2y+hlFAIIIIDA5ARSBbYOtg72odRMTZiUjl8FBXuLRM8xxb8Eds/4vdeqH//0x0/f/OHbex/jfgQQQACBGwToBR3sG6ExxWUd7Cnc8NNLhHT8Bm72DhQtJyH+JbBbRu/dRj0Xft/8z7dE9t0kPQABBBB4n0CqwE7RC6vXVwT2+3n74VdTOn4Flr1FoueY4t/VN4Ce0Xe9VVX4EdnX+8IbIIBATwK1zr617vP337291Opr9ZUfET8U0KkJk3IiNYIipMPJ3t7/rzuBPSLc5BWB1/sYkf0KjCkCCCBwEoHX6+zrR3YX2Cl6YfX6Sgf7dVZeOE85kSrE7C0SPccU/66+AfSMvuutelv4EdnX+8QbIIBALwJv19myrrvAVl/pYFes7xpTEyblRGoEgw72QNFyEuJfArtl9N5t1Hv7GJF9N1YPQAABBAaB99bZ57/sLrBT9MLq9ZUO9kjVaycpJ1JFmb1FoueY4t/VN4Ce0Xe9VbcKPyL7et94AwQQ6EHg1jrbXWCrr3SwD2VwasKknEiNoAjpcLLX72CPGDCJIXBrH3sGQGTHhAFDEUDggQRurbPdBXaKXli9gaGD/cDk3/PolBOpYsLeItFzTPHv2RvA8/+f7M/6BH7888/7kche38csQACBawmkCmz1lQ72ocxLTZiUE6kRFDrYA0XLSYh/zxbYt9a/ljESbhSRHR4AzEcAgbsI3NovdbDvwjrNzWfXVx9tmA72RxO/8XkpJ1JlPnuLRM8xxb9nbwC3CoaeUcIqIlsMIIAAAscI3Novuwts9ZUO9qGMSU0YHexD4bLOTSEd3eGQEHsJ7OFxk4MEiOyD4NyGAALRBOgF/8bNzAmggz2Jd1JOpAo3e4tEzzHFvwR2z/j9aKuI7I8m7vMQQGB1AqkCW32lg30od1MTRgf7ULisc1NIR3c4JMReAnt43OROAkT2nQDdjgACUQToBR3smQNeB3sS76ScSBVu9haJnmOKfwnsnvF7lVVE9lXkfS4CCKxGIFVgq690sA/lamrC6GAfCpd1bgrp6A6HhNhLYA+Pm5xEgMg+CaTHIIBAawL0gg72zAGugz2Jd1JOpAo3e4tEzzHFvwR2z/i92ioi+2oP+HwEEJidQKrAVl/pYB/KzdSE0cE+FC7r3BTS0R0OCbGXwB4eNzmRAIF9IkyPQgCBlgToBR3smQNbB3sS76ScSBVu9haJnmOKfwnsnvF7pVXE9ZX0fTYCCKxCIFVgq690sA/laGrC6GAfCpd1bgrp6A6HhNhLYA+Pm5xAgLg+AaJHIIBABAF6QQd75kDXwZ7EOyknUoWbvUWi55jiXwK7Z/xeYRVxfQV1n4kAAqsSSBXY6isd7EM5m5owOtiHwmWdm0I6usMhIfYS2MPjJncQIK7vgOdWBBCIJEAv6GDPHPg62JN4J+VEqnCzt0j0HFP8S2D3jN+PtIq4/kjaPgsBBLoQSBXY6isd7EM5nJowOtiHwmWdm0I6usMhIfYS2MPjJgcIENcHoLkFAQQQ+IkAvaCDPXMi6GBP4p2UE6nCzd4i0XNM8S+B3TN+P8Iq4vojKPsMBBDoSiBVYKuvdLAP5XRqwuhgHwqXdW4K6egOh4TYe7bA/vFPfxwITdYl8OOff96PxPW6vvXmCCAwBwF6QQd7jkh8/y10sN/n8uFXU06kCix7i0TPMcW/ZwvsntGQZ9Wtwu+ZBHGdFw8sRgCB8wncWmc/f//d+R820RPVVzrYh8IxNWF0sA+Fyzo3hXR0h0NC7CWwh8dNXhG4tY8R168gmSKAAAJ3ELi1znYX2Cl6YfX6Sgf7juQ+89aUE6lixt4i0XNM8e/qG0DP6LveqvcKP+L6er94AwQQ6EPgvXX22bruAlt9pYN9KItTEyblRGoERUiHk71+R2jEgEkMgbf7GHEd43qGIoDABxF4u87Wx3YX2Cl6YfUGhg52ZeTFY8qJVGFmb5HoOab4d/UNoGf0XW/V68KPuL7eH94AAQT6EXi9zr62rrvAVl/pYL+O96+epyZMyonUCAQd7IGi5STEvwR2y+i926jax4jru1F6AAIIIPAugVpn3/5ld4GdohdWr690sN9m5kVfp5xIFV72FomeY4p/V98Aekbf9VY9F37E9fV+8AYIINCXQKrAVl/pYB/K6tSESTmRGkER0uFkr9/BHjFgEkPg+f8z/+YP38bYy1AEEEDgownQC+qrj465PZ+ng72H1gO/N+VEqhCyt0j0HFP8q4PdM35ZhQACCCAwN4FUga2+0sE+lJmpCaODfShc1rlJx34dX+14UwJ7ByzfigACCCCAwEkE6AUd7JNC6SGP0cF+CNb9D005kSoy7C0SPccU/xLYPeOXVQgggAACcxNIFdjqKx3sQ5mZmjA62IfCZZ2bdLDX8dWONyWwd8DyrQgggAACCJxEgF7QwT4plB7yGB3sh2Dd/9CUE6kiw94i0XNM8S+B3TN+WYUAAgggMDeBVIGtvtLBPpSZqQmjg30oXNa5SQd7HV/teFMCewcs34oAAggggMBJBOgFHeyTQukhj9HBfgjW/Q9NOZEqMuwtEj3HFP8S2D3jl1UIIIAAAnMTSBXY6isd7EOZmZowOtiHwmWdm3Sw1/HVjjclsHfA8q0IIIAAAgicRIBe0ME+KZQe8hgd7Idg3f/QlBOpIsPeItFzTPEvgd0zflOtulWwpvJIsfvzD2t0hPb6Qzy/EEvz7+fvv9sbKkt9v/pqjfWKwJ4lrXQ4Z/HEY96Dfx/D9eKnEtgXO8DHn0qAIDkV5zIPSxNgyzjmpBdN8293gZ3yE6+r11fLCOz/+svfPn358uXT09OTEQdxIA+mWAduCZKuBc1J9Z7HTErgVjxP+rpe6yQCXdcr8fwSIGn+pRd66KRb+btKPC8jsJ+BEtc9koYf+bHLYdn//vbX75a4q2wA7768i7EEbhU0sUBCDO+6XonnlwBO8y+90KMZuXp9tY7A9jsVrbb6lN8hKaext0j0Glf/EaZe3mDNvQQIknsJrnl/mgBb00vH3zrNv91/RDylnly9viKwj69Z597pd3TP5Tnb0/h3No+c8j6rbwCnQPCQNgQI7Dau3GVImgDbBafBN6f5t7vA9jvY/pGzQ8vSrQ2+e8KknEhVULC3SPQcU/xLYPeM31Sr7L//aO36tPUqLZ759yV96YUey9jq8ayDPUsc6nDO4onHvAf/PobrxU9dfQO4GJ+Pn4xAmiAZ+EPW57T1Ki2e+fclo7sLbB1sHeyxd+2ZpC2IxSal48fe3h2SNP+mFTTlX2NPAvbf3utz2nqVFs/8+7IudxfYKXph9XjWwZ6lTgo5QR+42TtQtJyE+Hf1DaBl7DHqMIE0QTJAWa8Gik6TtHhO24/S/Dty03o1UMw8IbAn8U7KiVThZm+R6Dmm+DetoOkZrawqAqkFq/VqjR+5rDj92jEtntP2ozT/Vtxbr9ZYrwjsitirx5ATqYGZvQNFy0mIf9MKmpaxyqhBILVg9TuNaxSsI1C/cpIWz2n7UZp/R9irrwaKmScE9iTeSTmRKtzsLRI9xxT/phU0PaOVVUUgtWC1XhHYlQMrj2n7kfXKvxkxc74S2LN4J+REauBm70DRchLi37SCpmWsMmoQSC1YdbAJ7JEEC0/S9iPr1d8Xjtb//OqrxzOB/Z99/CHfkXKCXjDZWyR6jin+XX0D6Bl9rDpKILVgtV4R2EdzZqb70vYj65UO9kz59/ZdCOy3RK76OqTjN/Cyd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTlcCexLvpJygF272FomeY4p/0wqantHKqiKQWrBarwjsyoGVx7T9yHqlgz1zvhLYs3gnpOM3cLN3oGg5CfFvWkHTMlYZNQikFqw62AT2SIKFJ2n7kfVKB3vmdCWwJ/FOygl64WZvkeg5pvg3raDpGa2sKgKpBav1isCuHFh5TNuPrFc62DPnK4E9i3dCOn4DN3sHipaTEP+mFTQtY5VRg0BqwaqDTWCPJFh4krYfWa90sGdOVwJ7Eu+knKAXbvYWiZ5jin/TCpqe0cqqIpBasFqvCOzKgZXHtP3IeqWDPXO+EtizeCek4zdws3egaDkJ8W9aQdMyVhk1CKQWrDrYBPZIgoUnafuR9UoHe+Z0JbAn8U7KCXrhZm+R6Dmm+DetoOkZrawqAqkFq/WKwK4cWHlM24+sVzrYM+crgT2Ld0I6fgM3eweKlpMQ/6YVNC1jlVGDQGrBqoNNYI8kWHiSth9Zr3SwZ05XAnsS76ScoBdu9haJnmOKf9MKmp7RyqoikFqwWq8I7MqBlce0/ch6pYM9c74S2LN4J6TjN3Czd6BoOQnxb1pB0zJWGTUIpBasOtgE9kiChSdp+5H1Sgd75nQlsCfxTsoJeuFmb5HoOab4N62g6RmtrCoCqQWr9YrArhxYeUzbj6xXOtgz5yuBPYt3Qjp+Azd7B4qWkxD/phU0LWOVUYNAasGqg01gjyRYeJK2H1mvdLBnTtdlBPbMEL0bAggg8JrA5x96FqyvbTTvR+BWwdrPUha9JtB1vRLPL17m39fRbr46gVXimcBePdK8PwIITEdglQ1gOnBe6FICBMml+C/78K7rlXh+CSn+vSy1fPADCKwSzwT2A5zvkQggkE1glQ0g20usf0uAIHlLJOPrruuVeH6JX/7NyOMUK1eJZwI7JSLZiQACH0ZglQ3gw4D4oCUIECRLuOn0l+y6Xonnl1Dh39NTxgMvJLBKPBPYFwaJj0YAgZ4EVtkAetJn1VECBMlRcmvf13W9Es8vccm/a+ent/93AqvEM4H9737zFQIIIHA3gVU2gLsN9YBWBAiSVu78amO6rlfi+SUE+PerU8E3LkBglXieTmAv4FuviAACCCCAAAIIIIAAAggggMCGAIG9QeICAggggAACCCCAAAIIIIAAAvsJENj7mbkDAQQQQAABBBBAAAEEEEAAgQ0BAnuDxAUEEEAAAQQQQAABBBBAAAEE9hMgsPczcwcCCCCAAAIIIIAAAggggAACGwIE9gaJCwgggAACCCCAAAIIIIAAAgjsJ0Bg72fmDgQQQAABBBBAAAEEEEAAAQQ2BAjsDRIXEEAAAQQQQAABBBBAAAEEENhPgMDez8wdCCCAAAIIIIAAAggggAACCGwIENgbJC4ggAACCCCAAAIIIIAAAgggsJ8Agb2fmTsQQAABBBBAAAEEEEAAAQQQ2BAgsDdIXEAAAQQQQAABBBBAAAEEEEBgPwECez8zdyCAAAIIIIAAAggggAACCCCwIUBgb5C4gAACCCCAAAIIIIAAAggggMB+AgT2fmbuQAABBBBAAAEEEEAAAQQQQGBDgMDeIHEBAQQQQAABBBBAAAEEEEAAgf0ECOz9zNyBAAIIIIAAAggggAACCCCAwIYAgb1B4gICCCCAAAIIIIAAAggggAAC+wkQ2PuZuQMBBBBAAAEEEEAAAQQQQACBDQECe4PEBQQQQAABBBBAAAEEEEAAAQT2EyCw9zNzBwIIIIAAAggggAACCCCAAAIbAgT2BokLCCCAAAIIIIAAAggggAACCOwnQGDvZ+YOBBBAAAEEEEAAAQQQQAABBDYECOwNEhcQQAABBBBAAAEEEEAAAQQQ2E+AwN7PzB0IIIAAAggggAACCCCAAAIIbAgQ2BskLiCAAAIIIIAAAggggAACCCCwnwCBvZ+ZOxBAAAEEEEAAAQQQQAABBBDYECCwN0hcQAABBBBAAAEEEEAAAQQQQGA/AQJ7PzN3IIAAAggggAACCCCAAAIIILAhQGBvkLiAAAIIIIAAAggggAACCCCAwH4CBPZ+Zu5AAAEEEEAAAQQQQAABBBBAYEOAwN4gcQEBBBBAAAEEEEAAAQQQQACB/QQI7P3M3IEAAggggAACCCCAAAIIIIDAhgCBvUHiAgIIIIAAAggggAACCCCAAAL7CRDY+5m5AwEEEEAAAQQQQAABBBBAAIENAQJ7g8QFBBBAAAEEEEAAAQQQQAABBPYTILD3M3MHAggggAACCCCAAAIIIIAAAhsCBPYGiQsIIIAAAggggAACCCCAAAII7CdAYO9n5g4EEEAAAQQQQAABBBBAAAEENgQI7A0SFxBAAAEEEEAAAQQQQAABBBDYT4DA3s/MHQgggAACCCCAAAIIIIAAAghsCBDYGyQuIIAAAggggAACCCCAAAIIILCfwP8DgObxIIK3MuAAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\" width=\"246\" height=\"75\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call an integer rectangle as \"squarable\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003enon-unit squares of equal sizes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle can be broken into six \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e squares. Therefore, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle is squarable.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 88.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 44.25px; text-align: left; transform-origin: 384px 44.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 293px;height: 83px\" 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\" data-image-state=\"image-loaded\" width=\"293\" height=\"83\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInteger rectangles that are not squarable are called \"non-squarable\". The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 34.5px; height: 18px;\" width=\"34.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.5px 8px; transform-origin: 118.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32.5px; height: 18px;\" width=\"32.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e square units are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 774px; height: 18.5px;\" width=\"774\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 47.5px; height: 18px;\" width=\"47.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the program should output:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 668px; height: 18px;\" width=\"668\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.5px 8px; transform-origin: 247.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Reflections and rotations are not significant and should be counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function TA = nonSquarables(A)\r\n    TA = 8 * A + 8;\r\nend","test_suite":"%%\r\nA = 20;\r\nTA_correct = 168;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 200;\r\nTA_correct = 24732;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 2000;\r\nTA_correct = 3128803;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 20000;\r\nTA_correct = 382868578;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 200000;\r\nTA_correct = 44889840284;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nA = 2000000;\r\nTA_correct = 5150630032283;\r\nassert(isequal(nonSquarables(A),TA_correct))\r\n%%\r\nAs = 1000000:100000:5000000;\r\nTAs = arrayfun(@(A) nonSquarables(A),As);\r\nss = floor([TAs(1) TAs(end) sum(TAs) median(TAs) std(TAs)]);\r\nss_correct = [1237846589396 33831082399137 567489801806465 11849294784960 9910963238214];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('nonSquarables.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-23T12:36:30.000Z","updated_at":"2026-03-19T11:13:38.000Z","published_at":"2021-11-23T18:56:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAny integer-sided rectangle can be cut into unit rectangles (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\times1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) and rearranged into sets of smaller rectangles. For example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle can be broken as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                      \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"75\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"246\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe call an integer rectangle as \\\"squarable\\\" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enon-unit squares of equal sizes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\\\\times6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle can be broken into six \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\\\\times2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e squares. Therefore, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\\\\times6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle is squarable.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"83\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"293\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInteger rectangles that are not squarable are called \\\"non-squarable\\\". The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e square units are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{ 1\\\\times1,\\\\ 1\\\\times2,\\\\ 1\\\\times3,\\\\ 1\\\\times5,\\\\ 1\\\\times6,\\\\ 1\\\\times7,\\\\ 1\\\\times10,\\\\ 1\\\\times11,\\\\ 1\\\\times13,\\\\ 1\\\\times14,\\\\ 1\\\\times15,\\\\ 1\\\\times17,\\\\ 1\\\\times19,\\\\ 2\\\\times3,\\\\ 2\\\\times5,\\\\ 2\\\\times7,\\\\ 3\\\\times5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCreate a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the program should output:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eTotal\\\\ Area = 1+2+3+5+6+7+10+11+13+14+15+17+19+6+10+14+15=168\\\\ sq.\\\\ units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Reflections and rotations are not significant and should be counted only 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Sequences 77: Powers of Fibonacci Numbers","description":"Given integers  and , we are asked to evaluate the following function: . That is,  equals  raised to the power of the -th Fibonacci number. We define  as follows:  and  for .\r\n        Example:     .\r\nPlease reduce the output, modulo .\r\n------------------------\r\nHINT: One solution is already shown, however java math is not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 172px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86px; transform-origin: 407px 86px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 47px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23.5px; text-align: left; transform-origin: 384px 23.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven integers\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following function: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAAAyCAYAAADSinAfAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAApKADAAQAAAABAAAAMgAAAAB/Iko2AAAIz0lEQVR4Ae2ae6hVRRTGfaXXR6nli/JJpohhmpakmUjmo9QeVn8oCKaJUfTA/yIrTPGRYhZEGhYVFWgPK8tKy1eYUCmKIeIjDU3NV6VFalrf794913G79z5nzjn74DnNgu/O7Flr1sz+9tprZva5NWp48Qx4BjwDngHPgGfAM+AZ8Ay4MVDTzdxbewYqGWiov/2z4OKUbFZkYVdtUqe65iuegewZ+FemTYRZwlXCGWGJ8IdQIVwtXC8cEq4UvHgGisLASo1CcC6MGO1htX0U0Z7Y5DNkIj1emcAAsUMWRD6tKs77+6OuyKJePANFYaCfRiE7nhYus0bsrrpJdP6MYhHjq+kyMFXuCcjV1jDNVd8s1LLanKomkp06eWPPgBgYErBQX+VkoZUwXGD5PivkJDlHck6j+U7lwgCZ0OwfOdjUFpoJbYT3BS+egaIyMEqjsVz/Ktj7xG26zmvV9RlSDHpxZmBw0GO5SgITITDnC/9w4cUzUCwGCLz9AoE4pliD+nE8A3EM8FmHYAQcZMpC2IPsEi4twbsZrTmvEzqU4NwLMeV5ckIw/uzojMxq7y/rOfZPzZyflPgsMC61EdJ1DKl82mBDz2+2/yfhp0D2iCZDfqb6tQkEcPKeK6wSfhP4VNRVWC8QA+8KTgLxOIrCMbVvFZYKLwojhUzSWwb8B8i0TIYXub6R5rdB2CjwzwReohm4RM0887+F4wKfioiZpwR+4TksOEsX9SD4zFtBOUN4QCCwyBRGt0T1lkKUNFXjbuFDgfRd6sJ/sRwQov6xoNTvrZDzbytnxAcn8k1CZ4Gt2hlhrZCT0NEEHWnalsa62CkY/Re20qoTrLwV5bTMPar74b55Ob1EMzBezXDEUn9PYDI4aJsSXDsVpN0TgQMcswcMyxg1mIA8qTpLmi3mQ+qrdmMZ1Fmu9wnwE77nMri9gtzCInkhNpZZ3mYHbX2ttqyrNwedTcBFZbheIZuhIe9fBfr2ofZyuJwU3JvPkhc+zVpqOiKQpNpZ6s2qcy6xT92WOrn6nNQmGLfHmN5p2WA7wLJrozr7hS1WWzlV2WNzz2vK6aYKdC83Btx8YPnjjAFftLUQhgnVkk2EDqm2rlHjc6tuV+3US+Tznc7IaFV4U8iS2Qr/QTJQ6CEQzPMElkUj7EHQs7f92DTmUDZTH8YAvGwcuJB2wnCB1WCpkDR3To0cbvoJHYUdQilJmlwPCoh4zyKkT1Dfo5Ll/DFLl7HKf3UQEEQ0uF0ICxnioGBsXggZrA50I0LtcZczpeATgT0uew4jc1QxYxGkDYzCocTHXsH4oeTFQcYK+LV1N6BIkHekw/7BBJuLUZU217zIp4Um1s33Vx2uDgm89E5iDiM44FuS/fBr6nqAQHZAD9YLFYItP+kCHdkjG+kko0ZCa8EEBlkIeUKg7TVhl7BcyEX49HC/cEpgbpDWVODUzGlwrsAmHB14SEiSp6XEbkqSUYyOpetIAXBrjP+k5mJwHTV+ezXWiVJkantTBuahEJBkAsDD2i0YHRltusBDtYWgZUOLXVhn28XVWULNGINUZw4s14UQvh4wb/x/Ldwt/CUwDsJSYsYeUtkS/4cvD9jyorgKL5UZJ58y0xwzzStNrjONXa1PilKCyTwcOmwXyCz1BQJjo7BE2Cm8LRwVwsKSX1dg+WVv6SocFO4KOvF9k6WbshByk5yQiRFOfW8IE4QvBaRbVVH5d5NVj6qS4RCyuqvMUIfFrp0i7H+IaHNpSpNrl3nE2vaQxn5ju8daxiuuC3wcjjdJ1PQO+jOPPYK9ZUjsmIVyqmzM/eF7QajPtkC/JdQedUl2wtd3UcoSaUuT66wpqJVgaS8BB2WXKUtEuWK/h1RUFc5/ycJkY4QMwJJaKLGz/0k5fdxy3Fb1TsF1NhmZVQNh/1mqkibXWXOSbUCafU7WjgNDfsVAGgr1Kmtuf9hSmKBmiS2UXCFHPS1nE1W3g90OVrOEW+YXVPGH7K0qSvJvWlw7kcEkouQyNdoBkM1DifJDdjsksJfkof0iuAh7xmZBh1YqOwo7gut8ioHqbF5G7o1DjS23BRfMn71VJjFz3JvJMELPKbt/RLtrE18N+MySq6TFda7zOa8fBwmzv6IkGHKVDeqIj16ODobJnsPQy4KZy1hHH3HmCy2fQ0NGBCp7XsbM9kWcF9hPUukqZvUx95hraW+xXOeQJtdOc4nLkPbNbZHHA05ezzfeqksOSP2E789XxV61lIagmS3MECYKNQV8vC7wyeYl4UnhaHDN56AKYZnwp5AkZkkmexMQtjBXswSbgGQubwmrhCi5JWjMZZ/N/S2OcurYlusp25Vrx2nlb06GYGk1b+r8PF3y6w6+Pknww4txh3CNQFB9I3wrmBeGB42P/UHbKypZZglShJ8PzXx5MGw54qSLFMZ2QYQRhxujJzinCXzyaixECcv1WWGfYLYBUXYXS1u+XBf1PmprtCmCeSCUK4WGQq6CTwL8d8EEWNjXODWYMY+rTuZqZxlNt/T4OmLpCYJTlh4/7KfixA44lqqwzFKDmcta1Zl3t7CRdX2f6tg/b7VdzNV8uC7qfXXQaCcE8zDskgc+IY/ZzAz8jonxYR4qY7IE2wcqujC3kwL6YwJLty2LdWHP91lbGaovCmxZ1s3nGtuEjE7Gwx9Zr4+QJCukxDYpaJP6F1uXL9fFnm8q47WXVzINJ+S4LNlbukFCAyFKWqhxuNA8Sqm2TsJogeAYJeQjXdWZlyIqYG2//XXBeAR5KUm+XJfSvcbOdaQ0PLzxsRb5K9hbstwn7SHzH+WchzWq8pIVa7xzI/taQRiYIy/sEbsXxNs5J+wj5woswyPONadamyzvbCN6pjqKd54qAyzXHBTYm7Uu4Ejsb3cLhQ70uCmarcEjcQa+vXQY4DPJOmGTULtA02bJvLxAvjK56SsDfsF5JpOh15cOA3U11XsFltpSk86acKaTd6ndk5+vZ8Az4BnwDHgGPAOeAc+AZ8Az4BnwDHgGPANlx8B/32VHPgsG9C8AAAAASUVORK5CYII=\" width=\"82\" height=\"25\" style=\"width: 82px; height: 25px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. That is, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equals\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e raised to the power of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eFibonacci number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAAoCAYAAAACCDNUAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAmKADAAQAAAABAAAAKAAAAAD5mAbDAAAFTElEQVR4Ae2aaahVVRTHn6X5Mips0AbsvSDLoMkKbcAShZIEqQ+lghFC04eKIIIkoZHwQ1hE0IeiCSMoCoPKRhD8EkUhZIMV+BREoyIiy542/f56F2x3Z7hnuPnOuWvB/+55nbX/d+119t73Dgy4OAPOgDPgDDgDzoAz4Aw4A86AM+AM9D0DwzCwGhyXx8S4nA5raF8I8volqbmbyqeTGhpWdz72rgMTS9j9I2NOKzFurA6ZhmErwXIwAUwH34FUGZ/asr9hGclksBZctr9q3+cGPt8GvwDpOBKcDi4FRugO8m2Qz5jECWAREA8mo2SeANvA32AQTAFyyDmdcib59GmKnIyhK8BN4LBeGP0kSv/p4FdSOVSSyNneAuo7NalDg+v0OjAOlD6QMRctNDndUxl9mtT0GsY+BK4He4HxYMGEqmqynuGm9I0cVfLyrTl9mtg8F6ONA6UzcyaxnXa9Stomm5iQ8ZDrYId0MftJ9Lko6PdOkE/KauV+ktTQ8Lr5gf07yW8MyknZtvKwK2myVequYrB5rNLhLpQd2kWfpnX5GIONh+e7ML6NHGjaHwHjoZYIdmVA5mbyI0FZWW2AdVo6WoWO/GWZlqTaf10QzCUpij9K+6qgT9s4CKZWb1ZOZR77eKRar9iXgVZ3m2UpkzMO5DjHRpM9j/IoULRvuxSKYDr1Zckwjbp+MPmezCygU+SZ4BowD9wDeiWzUawrkaryKQquKKkkjOI/oGMIzACK3heC28Bu8AHolbyO4strUH4dOj6sQU9XKvIcLCRWCh9J0apjbK9ENh5Tg/KjKugIHVPXL3LWWF6iYk9cWWNZi7oOHibUaFOuqiIOtgFtd4FBoD3JuWAl+BL08kLxC/TfAqqKLkTLyDkMOjEYuIz8FjAJTAOyTVFWEaaXov3dqzU8IGlx1KC2uAo5n27qbe8h54rlKyruiytbVtZPXsbBz+Tj0+Fi6n4Dh4N+kEJ7sKx7sIthK3ytvJvA3hTqunk9ar/2ApicoGOsVy0IDNTeRZv8UMTBOrA7rAzy4vhG8CJ4E9wPpoO+l4dhwFaubqVjEXEr4sqoLCLXAH0p0qVNcZPkCIwdBcbDzQnGz6VOPw0liaLde8DGW6prHR0OmiiFIljWBHUbb4Q8l9Uxo+1W2uaB34F0lXGw2Yz7qQboiy4qCxlgHCgdKqjgDvp/Da4GinQ3gE1AuhQNi4j2eHXwML/IQxP61uJg2sRb1BEZSxIeVKTqWzpLTxkHU3TQ2KoQMUVF/5aw58pRioruB8+KBs2gLJ1/gIlRW1bxfRrNlirpgqyHdNFWyMHGpyjUsVyvQIkm08v7nX0Pyfg4mKfI8MsoGgHHMadngSJWKHLUXeBPsDdsyMmvon0snCI1r8qi8G2rRF9wVakSwao+u+z4OQw0DpReW1ZRNO6kjt61UX1TiiMd+8VJHJ3/MweLUmHDIgraN5nocm+qFfok1en5wWiuZ1CuY/XKcSU6/DRJdGC5EwwFRi8nX+ji9hsGhKvW8tqPVYlkTYpgS5jrnhQedC+4FFSR9Qx+poqCgzBWr2e91s0fwlScxNuA/93EJjlYL8m5HeWfg365lO0llwfodgcbGNCBYQsYOoAZL9TCQL872CWwKOfSPi6UwbDg+fIM9LOD6b9iI2BmRJ/+oKnL7Fa/LtPuwSIuKhWPZ/SpHQ2nkO6spK1ZgxWx7DfcxwLTxfvZ4BWQ9htm0N2zaQzcS8M2YKeOzeRXp3VuWb2ugLYCm3tSOqtlc/bpOAPOgDPgDDgDzoAz4Aw4A86AM+AMOAPOgDPgDDgDfcnAvxO0U9bq9HypAAAAAElFTkSuQmCC\" width=\"76\" height=\"20\" style=\"width: 76px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"33.5\" height=\"18\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.5px; text-align: left; transform-origin: 384px 12.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        Example:     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"162\" height=\"25\" style=\"width: 162px; height: 25px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease reduce the output, modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93.5\" height=\"20\" style=\"width: 93.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e One solution is already shown, however java math is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = P(x,n)\r\n    import java.math.BigInteger    \r\n    m = 2178309;   \r\n    p = BigInteger(num2str(x)).modPow(fiboBig(n),BigInteger(num2str(m))).longValue();\r\n\r\n    function f = fiboBig(a)\r\n        if a == 0\r\n            f = BigInteger.ZERO;\r\n        else\r\n            fs = [BigInteger.ONE BigInteger.ONE];\r\n            for i = 3:a\r\n                fs = [fs(2) fs(1).add(fs(2))];\r\n            end\r\n            f = fs(2);\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nx = 3; n = 6;\r\np_correct = 6561;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 10; n = 10;\r\np_correct = 1704349;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 11:20; n = x.*10;\r\np_correct = [1789328 703074 1326793 1022378 1427238 485143 399395 1317366 1490422 632477];\r\nassert(isequal(arrayfun(@(i) P(x(i),n(i)),1:length(x)),p_correct))\r\n%%\r\nx = 50; n = 50;\r\np_correct = 2101373;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 1234; n = 5678;\r\np_correct = 1816441;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 11111; n = 11111;\r\np_correct = 1606418;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 99999999; n1 = 3200055; n2 = 1185207;\r\np_correct = P(x,n1);\r\nassert(isequal(P(x,n2),p_correct))\r\n%%\r\nx = 123456789; n = 123456789;\r\np_correct = 1611366;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = 1e12; n = 1e12;\r\np_correct = 1935991;\r\nassert(isequal(P(x,n),p_correct))\r\n%%\r\nx = setdiff(primes(1000),primes(100)); n = x.^2;\r\np = arrayfun(@(i) P(x(i),n(i)),1:length(x));\r\ns_correct = [828561 675946 113 717102];\r\nassert(isequal(floor([mean(p) median(p) mode(p) std(p)]),s_correct))\r\n%%\r\nfiletext = fileread('P.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2022-10-19T20:51:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-10-19T20:51:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-18T16:04:17.000Z","updated_at":"2026-03-23T13:00:56.000Z","published_at":"2022-10-18T17:04:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven integers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following function: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x,n)=x^{F_n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e raised to the power of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. We define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_1=F_2=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_i=F_{i-1}+F_{i-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u0026gt;2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        Example:     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(3,6)=3^{F_6}=3^8=6561\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease reduce the output, modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{32}=2178309\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e One solution is already shown, however java math is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52809,"title":"Easy Sequences 28: Sum of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the sum of the radicals of all positive integers . \r\nFor , the radicals are: . Therefore, the output should be '41'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABq0lEQVRYhe2XXZWEMAxGrwcc1AAGUIACHIyDcTAW0IAEPGABDViYfaA5W5gG+rdnH6bfOXkYpgm5pUkAqqqqqr5RBmgifTprbaRf6/iebbS5JMnYAO/ApBpnvWsb8Aj03zz+YnNc+npSdzDmJpE38LqJ8bzx72JBehu0B5YImBlYgcG51vK5Kb3iL08l5Akmyd2pK5jeJqKtceNMypqHjZFcE3cKhZm43tHGibMpa1b2k9AR32yCFAoT0mVmdJiBz/pY7PViYKEwIRIYX0da0Yt+I6HwfSoJIwlrx7Fjr70XfjitcQSrFIyxMVbCC3zg2Oo3Mo9cKRiJE9t2G47j4ZmRQxEYmR9J05vjME6NAZSBmdh3N+eIyODV2nqQcmEe7HWS2zx6/hlmoAwI7J1OGkiyUmFKgsDvkxlzgqTA9NyDtMS9g0nNZM2aWJiW+4kt7dY4vzt0OJlRWZ0M4mAEZLF+mq2nxNzB+OTY9QR8Cbj/pQzH14qrgSUgVx9W2qvJfPpvtfd62ZgjGW3d2ECzx0b8U3xS1vts8iQ3nGKMFujPvm2qqqqqqqq+Uj8xKNuJDs64CAAAAABJRU5ErkJggg==\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.5px 8px; transform-origin: 182.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the sum of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e'41'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumRadicals(n)\r\n    s = 41;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 41;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 3512;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 351964;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nns = 1000:5000;\r\nss = arrayfun(@(n) sumRadicals(n),ns);\r\nss_correct = [14572533416 1407530 2206262 3168720 4321316 5635156 7128944 8813000 2478567];\r\nassert(isequal([sum(ss) ss(1000:500:4000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 35252550;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 3522204030;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 352218412502;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nfiletext = fileread('sumRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:12.000Z","updated_at":"2025-12-22T17:26:46.000Z","published_at":"2021-09-27T10:53:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the sum of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'41'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52814,"title":"Easy Sequences 27: Product of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the product of the radicals of all positive integers . Since, the radical product can get huge fast, please output only the number of digits of the product.\r\nFor , the radicals are: , their product is . Therefore, the output should be '6' digits","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the product of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110px 8px; transform-origin: 110px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, their product is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAkCAYAAACDr7TyAAAC+UlEQVRoge2aXbWsMAyFtwccYAADKEABDo4DHGBhNIyE8TAW0ICFuQ9tFqG3LQmlzFn35lurL3OaJuzQ9IcDGIZhGIZhGEYtWgCNon8HoE+0hx+vht8ztNhiO+OLbKXPdJVtkhZO5A9cIiQ0AFZvE2uvSn61DACWRHxHIlJ8K4DJt8XbHsVbYpulwSYaNemAE9IJ+8C9WTX8apgPYlyRTlzn/74EsTXYXoKhgm2WAU74AcAbOvFolv3c7FdD78flZboBMGI/894RWy5u7Blp7A/+LrUltir4rJGI94P8W1rLr4Y3XMJihKU99E1x5Z6REvO80FaFVrwFTpSzi/pZv1I6uBhzsfHSGc4ISmhsFhK8vHM/JbYqNOKNrC8vMeOJAGolbcBx6eZlivcd2O+pmQpvQ/3GC2zVaMSL7cT4wp7bgJT4vRqeNB4zjymXeG5PCSqxVaMVr4d7q2bEkyjdGX0zaVQxwjL6hF54KoUltmpKxRuxX9hXyErlN5NG68oU/P6CXvj1Als1V4jXYL+FD8Wo5fcMtHuMbVa48Ecx5ZKmtVVzlXgtthknuRH5VtLIb2z95cIfXRDkkqa1VXOleFR2JMF8I2kd8ru2/6o8ErTt/Y1Jo9uKWRiTVHg6JJfYqrlSPApoudnvEbTm5hIG7M+hUuFpzBJbNTVmmuT8cVfSpAkD3LosmQU8djrilNiqqbGmSYK5K2mShPF4aW3KVYsn68N3oCW2KqTiNch/zKM3TbJz1PiF9ztBf132EMQzYl8ZUrclBN/9hWWwxFaFVDx+gJ6wF49K0PtgjDN+ednRLN4062dsHyLDRn1CgelCOeaL4k69DCW2Ilrsr6Jyh2K+paXpPfkgVzgBpLNA47fD3u8Hx5+Fwo+suZa6SuJJp+eiy94X8s9aYpuk9QO+Iu2B9NQd4d4g3neC7v9BzvidfB+6dcn5GxLjp1rupr0P4p0h3zyU2P5T9JAdJ4xfxBOFC7hxLw8UHEaN+xlR8JXXMAzDMAzDEPAHvaP26LcvqHsAAAAASUVORK5CYII=\" style=\"width: 54.5px; height: 18px;\" width=\"54.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e6'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = prodRadicals(n)\r\n    r = 6;\r\nend","test_suite":"%%\r\nn = 10;\r\nr_correct = 6;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000;\r\nr_correct = 2263;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nns = 10000:50000;\r\nrs = arrayfun(@(n) prodRadicals(n),ns);\r\nss_correct = [4503407257 70876 91001 111568 132490 153727 175243 196990 47696];\r\nassert(isequal([sum(rs) rs(10000:5000:40000) floor(std(rs))],ss_correct))\r\n%%\r\nn = 1000000;\r\nr_correct = 5238328;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000000000;\r\nr_correct = 8237674403;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = intmax;\r\nr_correct = 18403071064;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nfiletext = fileread('prodRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:14.000Z","updated_at":"2025-12-25T20:09:26.000Z","published_at":"2021-09-27T10:28:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the product of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, their product is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e151,200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57839,"title":"Easy Sequences 104: One-line Code Challenge - GCDs of Sum of Consecutive Cubes","description":"For a natural number, n, the function CC(n) is defined as follows:\r\n                \r\nIn other words, CC(n) is the sum of cubes of all integers from 1 to n.\r\nGiven positive integers x and y, write a function that calculates the value of gcd(CC(x),CC(y)) . For example:\r\n\u003e\u003e CC = @(n) sum((1:n).^3);\r\n  \u003e\u003e gcdCC = @(x,y) gcd(CC(x),CC(y));\r\n  \u003e\u003e gcdCC(5,10)\r\n        ans = 25\r\nThe following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nRegular expressions are not allowed.\r\nOnly 'pure' matlab functions/commands are allowed (no java, no python).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 372.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 186.2px; transform-origin: 407px 186.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a natural number, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43px 8px; transform-origin: 43px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eCC(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 95.5px; height: 45px;\" width=\"95.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn other words, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eCC(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the sum of cubes of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140px 8px; transform-origin: 140px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, write a function that calculates the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 64px 8.5px; transform-origin: 64px 8.5px; \"\u003egcd(CC(x),CC(y))\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47px 8px; transform-origin: 47px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e . For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; CC = @(n) sum((1:n).^3);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; gcdCC = @(x,y) gcd(CC(x),CC(y));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; gcdCC(5,10)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        ans = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 116.5px 8px; transform-origin: 116.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function g = gcdCC(x,y)\r\n    g = gcd(sum((1:x).^3),sum((1:y).^3))","test_suite":"%%\r\nx = 5; y = 10;\r\ng_correct = 25;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = 123; y = 1968;\r\ng_correct = 60516;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = [123 456 789]; y = [987 654 321];\r\ns_correct = 18;\r\nassert(isequal(mean(gcdCC(x,y)),s_correct))\r\n%%\r\nx = 2000; y = 7337;\r\ng_correct = 4004001;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = [11111 22222 33333 44444]; y = [66666 77777 88888 99999];\r\ns_correct = 112466886431;\r\nassert(isequal(sum(gcdCC(x,y)),s_correct))\r\n%%\r\nx = primes(100000); y = x * 2 + 1;\r\ns_correct = 7455917221644;\r\nassert(isequal(sum(gcdCC(x,y)),s_correct))\r\n%%\r\nx = 123456789; y = 987654321;\r\ng_correct = 81;\r\nassert(isequal(gcdCC(x,y),g_correct))\r\n%%\r\nx = 1:10000; y = x * 3 - 4;\r\ng = gcdCC(x,y);\r\ns_correct = [87238 174316 261586 349208 435182 522452 610074 697344 783270 870508];\r\nassert(isequal(arrayfun(@(i) sum(g(1:i)),1000:1000:10000),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nx = [234567891 345678912 456789123]; y = [876543219 765432198 654321987];\r\ng = gcdCC(x,y);\r\ns_correct = [175689 135837 -96957];\r\n[sum(g) diff(g)]\r\nassert(isequal([sum(g) diff(g)],s_correct))\r\n%%\r\nfiletext = fileread('gcdCC.m');\r\nnot_allowed = contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regex') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\ndeblank(strtrim(splitlines(filetext)))\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-28T12:01:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-27T11:07:50.000Z","updated_at":"2025-04-24T23:46:15.000Z","published_at":"2023-03-28T11:58:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a natural number, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCC(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eCC(n) = \\\\sum_{i=1}^n i^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn other words, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCC(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the sum of cubes of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that calculates the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(CC(x),CC(y))\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e CC = @(n) sum((1:n).^3);\\n  \u003e\u003e gcdCC = @(x,y) gcd(CC(x),CC(y));\\n  \u003e\u003e gcdCC(5,10)\\n        ans = 25]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57805,"title":"Easy Sequences 105: One-line Code Challenge - IPv4 Address Validation","description":"The Internet Protocol version 4 (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\r\nIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\r\nFor example, the following are valid IPv4 address:\r\n    '123.123.123.123'\r\n    '0.255.001.010'\r\nBut the following are invalid addresses:\r\n    '0123.123.123.123'\r\n    '123. 23.123.123'\r\n    '123.123'\r\n    '123,123.123.123'\r\n    'abc.123.123.123'\r\n    '123.456.789.111'\r\n    'i like matlab'\r\nThe following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nRegular expressions are allowed.\r\nOnly 'pure' matlab functions/commands are allowed (no java, no python).\r\n---------------\r\nNOTE:\r\nThis would be the last of my one-line challenges.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 603.067px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 301.533px; transform-origin: 407px 301.533px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Internet_Protocol_version_4\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eInternet Protocol version 4\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.5px 8px; transform-origin: 279.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156px 8px; transform-origin: 156px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the following are valid IPv4 address:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 60px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 60px 8.5px; \"\u003e'0.255.001.010'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 8px; transform-origin: 123px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut the following are invalid addresses:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 143.033px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 71.5167px; transform-origin: 404px 71.5167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; tab-size: 4; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 72px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 72px 8.5px; \"\u003e'0123.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123. 23.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 36px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 36px 8.5px; \"\u003e'123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123,123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'abc.123.123.123'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 68px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 68px 8.5px; \"\u003e'123.456.789.111'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 60px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 60px 8.5px; \"\u003e'i like matlab'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e---------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis would be the last of my one-line challenges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = is_IPv4(s)\r\n    b = all(s\u003e=0 \u0026 s\u003c=255);","test_suite":"%%\r\ns = 'i like matlab';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '123.123.123.123';\r\nb_correct = true;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '123.123...123.123';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'0.255.001.010' '0123.123.123.123' '123. 23.123.123' '123.123' '123,123.123.123' 'abc.123.123.123' '123.456.789.111'};\r\nb_correct = [1 0 0 0 0 0 0];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'75.255.003.4' 'A.B.C.D' '000.000.000.000'};\r\nb_correct = [1 0 1];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = '0.00.000.0000';\r\nb_correct = false;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'1(1.111.111.1)1' '{1.1.1.1}'};\r\nb_correct = [0 0];\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\ns = {'111.222.33.44'};\r\nb_correct = true;\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\nn = randi(300,1,4);\r\ns = strjoin(arrayfun(@num2str,n,'uni',0),'.');\r\nb_correct = all(n\u003c=255);\r\nassert(isequal(is_IPv4(s),b_correct))\r\n%%\r\nfiletext = fileread('is_IPv4.m');\r\nnot_allowed = contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":6,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-30T11:04:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-03-30T08:54:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T17:19:11.000Z","updated_at":"2025-12-08T10:44:27.000Z","published_at":"2023-03-29T18:51:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Internet_Protocol_version_4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eInternet Protocol version 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (IPv4) is the dominant protocol for routing devices over the internet. IPv4 addresses are usually represented by four 1-byte decimal numbers (0 to 255) separated by three dots.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this exercise, we are asked to check whether a given string of characters is a valid IPv4 address or not\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Leading zeros are allowed, however each byte should only contain at most 3 characters, with no spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the following are valid IPv4 address:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    '123.123.123.123'\\n    '0.255.001.010']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut the following are invalid addresses:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    '0123.123.123.123'\\n    '123. 23.123.123'\\n    '123.123'\\n    '123,123.123.123'\\n    'abc.123.123.123'\\n    '123.456.789.111'\\n    'i like matlab']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly 'pure' matlab functions/commands are allowed (no java, no python).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e---------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis would be the last of my one-line challenges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53119,"title":"Easy Sequences 53: Greatest Proper Divisor","description":"The greatest proper divisor () of an integer  is the largest integer , such that  and . Furthermore, we define: . \r\nBelow is the set of 's of numbers from  to :\r\n                                .\r\nGiven an integer , create a function that outputs the sum of 's of all integers from  to , inclusive. For , your function should return, .\r\nTIP: Good algorithms for finding GPD's for numbers  to , can be found in Rosetta Code.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe greatest proper divisor (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e) of an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the largest integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37\" height=\"19\" style=\"width: 37px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Furthermore, we define: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79\" height=\"19\" style=\"width: 79px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eBelow is the set of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e's of numbers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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\" width=\"486\" height=\"19\" style=\"width: 486px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, create a function that outputs the sum of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18\" style=\"width: 34px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e's of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, inclusive\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, your function should return, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eTIP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e: Good algorithms for finding GPD's for numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, can be found in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://rosettacode.org/wiki/Largest_proper_divisor_of_n\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRosetta Code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"the function s = sumGPDs(n)\r\n    y = x;\r\nend","test_suite":"%%\r\nn = 25;\r\ns_correct = 107;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 1691;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 16507016;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 10000000;\r\ns = arrayfun(@(i) sumGPDs(i),1000000:100000:n);\r\nss = floor([mean(s) median(s) mode(s) std(s)]);\r\nss_correct = [6131600733080 4992760161090 165051503014 4903597092814];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 87654321;\r\ns_correct = 1268119158203109;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nn = 100000000;\r\ns = arrayfun(@(i) sumGPDs(i),10000000:10000000:n);\r\nss = floor([mean(s) median(s) mode(s) std(s)]);\r\nss_correct = [635439507299878 503400239949103 16504975497498 564032070925422];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 123456789;\r\ns_correct = 2515609811020846;\r\nassert(isequal(sumGPDs(n),s_correct))\r\n%%\r\nfiletext = fileread('sumGPDs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-25T04:32:21.000Z","updated_at":"2026-03-19T13:00:12.000Z","published_at":"2021-11-26T07:30:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe greatest proper divisor (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the largest integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\ |\\\\ x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026lt;x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Furthermore, we define: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD(1)= 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBelow is the set of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's of numbers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ 1,\\\\ 1,\\\\ 2,\\\\ 1,\\\\ 3,\\\\ 1,\\\\ 4,\\\\ 3,\\\\ 5,\\\\ 1,\\\\ 6,\\\\ 1,\\\\ 7,\\\\ 5,\\\\ 8,\\\\ 1,\\\\ 9,\\\\ 1,\\\\ 10,\\\\ 7,\\\\ 11,\\\\ 1,\\\\ 12,\\\\ 5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create a function that outputs the sum of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eGPD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e's of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, inclusive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, your function should return, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e107\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTIP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Good algorithms for finding GPD's for numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, can be found in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://rosettacode.org/wiki/Largest_proper_divisor_of_n\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRosetta Code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52849,"title":"Easy Sequences 34: Modified Pascal's Triangle","description":"Consider the integer triangle below:\r\n                                                                    \r\nIt follows the same rule as Pascal's Triangle, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \r\nGiven a number  find , which is the sum of the n-th row. Hence,  and . \r\nWe could be getting large numbers here, therefore please concatenate the total number of digits with the last 3 digits of  and output a single concatenated integer. For example the , hence the output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 347px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the integer triangle below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 164px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                                                    \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"167\" height=\"158\" style=\"vertical-align: baseline;width: 167px;height: 158px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt follows the same rule as \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pascal's_triangle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePascal's Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e find \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30.5\" height=\"19\" style=\"width: 30.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, which is the sum of the n-th row.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Hence, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"19\" style=\"width: 56.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWe could be getting large numbers here, therefore please \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003econcatenate the total number of digits with the last 3 digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30.5\" height=\"19\" style=\"width: 30.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and output a single concatenated integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, hence the output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 5;\r\ns_correct = 2030;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 55;\r\ns_correct = 17966;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 666;\r\ns_correct = 201462;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 7777;\r\ns_correct = 2342270;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 88888;\r\ns_correct = 26758054;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = double(intmax);\r\ns_correct = 646456993326;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = double(1e12);\r\ns_correct = 301029995664374;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nns = 10000:100000;\r\nss = arrayfun(@(n) S(n),ns);\r\nss = [sum(ss) ss(1:12345:end)]\r\nss_correct = [1490204856374 3011374 6727830 10443222 14159366 17876174 21592430 25308422 29024766];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-02T17:26:33.000Z","updated_at":"2026-02-07T14:04:07.000Z","published_at":"2021-10-02T19:50:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the integer triangle below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"158\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"167\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt follows the same rule as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pascal's_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePascal's Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e find \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is the sum of the n-th row.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Hence, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(1)=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(4)=14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe could be getting large numbers here, therefore please \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003econcatenate the total number of digits with the last 3 digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and output a single concatenated integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(5) = 30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hence the output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2030\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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Sequences 78: Trailing Zeros of Factorial Numbers at any Base","description":"Given an integer  and a number base , write a function that calculates the number of trailing zeros of the factorial of  when written in base-.\r\nFor example, for  and , the function should return , because:\r\n  \u003e\u003e dec2base(factorial(15),4)\r\n  \u003e\u003e   '103001313131311200000'\r\nFor  and , the function should return .\r\n  \u003e\u003e dec2base(factorial(10),12)\r\n  \u003e\u003e   '1270000'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.45px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 12.6px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 188.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 94.1px; transform-origin: 407px 94.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 7px; transform-origin: 48.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5px 7px; transform-origin: 59.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a number base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224px 7px; transform-origin: 224px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, write a function that calculates the number of trailing zeros of the factorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 7px; transform-origin: 19px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when written in base-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 7px; transform-origin: 49px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 16px;\" width=\"33\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79px 7px; transform-origin: 79px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 7px; transform-origin: 30.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, because:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 36.8px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 18.4px; transform-origin: 404px 18.4px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 105px 7.5px; tab-size: 4; transform-origin: 105px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; dec2base(factorial(15),4)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 105px 7.5px; tab-size: 4; transform-origin: 105px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24.5px 7.5px; transform-origin: 24.5px 7.5px; \"\u003e  \u0026gt;\u0026gt;   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 80.5px 7.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 80.5px 7.5px; \"\u003e'103001313131311200000'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 7px; transform-origin: 11.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39.5px; height: 16px;\" width=\"39.5\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79px 7px; transform-origin: 79px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 36.8px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 18.4px; transform-origin: 404px 18.4px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108.5px 7.5px; tab-size: 4; transform-origin: 108.5px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; dec2base(factorial(10),12)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 7.5px; tab-size: 4; transform-origin: 56px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24.5px 7.5px; transform-origin: 24.5px 7.5px; \"\u003e  \u0026gt;\u0026gt;   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 31.5px 7.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 31.5px 7.5px; \"\u003e'1270000'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function z = trZerFac(n,b)\r\ny = x;\r\nend","test_suite":"%%\r\nn = [15 10]; b = [4 12];\r\nz_correct = [5 4];\r\nassert(isequal(arrayfun(@(i) trZerFac(n(i),b(i)),1:2),z_correct))\r\n%%\r\nn = 3:3:45; b = 2:2:30;\r\nz_correct = [1 2 4 3 3 8 3 5 6 7];\r\nassert(isequal(arrayfun(@(i) trZerFac(n(i),b(i)),1:10),z_correct))\r\n%%\r\nn = randi(13)+2; b = randi(34)+2;\r\nz_correct = find(flip(dec2base(factorial(n),b))-'0',1,'first') - 1;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 30:3:450; b = 20:2:300;\r\nz = arrayfun(@(i) trZerFac(n(i),b(i)),1:numel(n));\r\ns = floor([sum(log(z)) sum(z) median(z) std(z) sum(tand(z))]);\r\ns_correct = [346 2562 12 17 91];\r\nassert(isequal(s,s_correct))\r\n%%\r\nn = 100; b = 25;\r\nz_correct = 12;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 1234; b = 30;\r\nz_correct = 305;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345; b = 35;\r\nz_correct = 2054;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 123456; b = 40;\r\nz_correct = 30860;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 1234567; b = 123;\r\nz_correct = 30862;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345678; b = 1234;\r\nz_correct = 20041;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nn = 12345678910; b = factorial(10);\r\nz_correct = 1543209860;\r\nassert(isequal(trZerFac(n,b),z_correct))\r\n%%\r\nfiletext = fileread('trZerFac.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java')...\r\n    || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'if') || contains(filetext, 'switch');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-11-06T10:21:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2022-10-26T10:06:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-25T12:04:07.000Z","updated_at":"2022-11-06T10:21:12.000Z","published_at":"2022-10-26T09:25:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a number base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that calculates the number of trailing zeros of the factorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e when written in base-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=4\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, because:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e dec2base(factorial(15),4)\\n  \u003e\u003e   '103001313131311200000']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e dec2base(factorial(10),12)\\n  \u003e\u003e   '1270000']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57417,"title":"Easy Sequences 86: The \"real\" Hyperprimorials","description":"In Easy Sequences 85, we define the hyperprimorial of , as a exponent ladder of primes numbers from the -th prime down to first prime (). OEIS, however, defines hyperprimorial differently. In OEIS sequence #A076265, the hyperprimorial of , ()  defined as follows:\r\n                             \r\n                             where:  is the -th prime number.\r\nUsing the above formula, we want to calculate , which is the sum of all hyperprimorials from 1 to n:\r\n                            \r\nFor example:\r\n                            \r\n                                \r\n                                .\r\nSince this will involve large integers, please output a vector containing first 6, last 6, and the number of digits of . Therefore, the final function output should be:  .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 430px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 215px; transform-origin: 407px 215px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.5px 8px; transform-origin: 7.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57412-easy-sequences-85-hyperprimorials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eEasy Sequences 85\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103px 8px; transform-origin: 103px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we define the hyperprimorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as a exponent ladder of primes numbers from the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime down to first prime (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 221.5px 8px; transform-origin: 221.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). OEIS, however, defines hyperprimorial differently. In OEIS sequence \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A076265\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#A076265,\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5px 8px; transform-origin: 13.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe hyperprimorial of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAACe0lEQVRYR+1Xu04dMRDlfkKAL0hoEAVICaKBAhpQElEhhdQUPAokGpCABomHyAeEUFADLVIQiIICOh4KFQ3QQcXrD+AcyYOG3bueO9zcFcVaGtm7HnuOj+2ZcanunZbSO8VVVwDz7kzB2P9mrNOY8Ab9V0GnAXVzRF/rmjitrSSwFsgS5IOabRftecg55E4B60B7DvJF6V6iPQvZU7pVA5MJdtDoDR8E1ReZmYs5UP1taJ+ZSBIKFmOifoHGp/DxE/VGxNAg+tZDP9lq8oKifiXAPkKPBqQQoJyrcjZ/4+do6FhBPVYrYF4GNLvfAGq7VsA0A4swMhMxlGS3EbpyOVz4KtnKe8woN9JiYBi6fwKCY9TtLjRK2QLWCt1/St9igJfiR9CfQv2rVsCSDEwYhrYUu11oH9YKmGbAa8Pajeh81uAnNdpiYBK6y0HfcsLmImPAkh7cWsQRrEkoGkF71bQeUYgZW8C46TB2EzX9WVZhAL9VnW8KQ3ryGDAPA18x6d8w8QPq+mrY4tgsYF4GtBO22K0IcxYwLwOeIF8VME8g9gb5qoB5GNBOOCvNIfgBSA+EadA45Dq4F+Z5qRhcbiu1Ia4udvUZsvYhEksZH5lEZgVu+kWCJ7DvELoUhrzUgjQwrmoI8rkM1yf4twaRPEwzkFR/xI9TSDJOStyl82WRPI2gUg7ZcpplML75l+wE3Uk/hHFUcr3UruQJTN4NOquVS5ZyyHkC4/kiW90QeZzwkrHwdfXqXOYFTOKudr7iZsigxNWX11RewCTz0GdJzhz/8WIQXO7AGHf5umL2ITdbogtdDBPQV0llXoy5r3IBzEtZwVjBmJcBr/4zAg2BKR/A8vQAAAAASUVORK5CYII=\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 76px; height: 45px;\" width=\"76\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                             where: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.5px 8px; transform-origin: 55.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 163px 8px; transform-origin: 163px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eUsing the above formula, we want to calculate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, which is the sum of all hyperprimorials from 1 to n:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 74px; height: 45px;\" width=\"74\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" 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style=\"width: 441.5px; height: 19.5px;\" width=\"441.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 190px; height: 18px;\" width=\"190\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115px 8px; transform-origin: 115px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince this will involve large integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264px 8px; transform-origin: 264px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eplease output a vector containing first 6, last 6, and the number of digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.5px 8px; transform-origin: 152.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, the final function output should be:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 163.5px; height: 20px;\" width=\"163.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    s = sum(hyp(n),1e6);\r\nend","test_suite":"%%\r\nn = 5;\r\ns_correct = [793011 987612 23];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 10;\r\ns_correct = [210753 400112 157];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 25;\r\ns_correct = [331784 287612 1846];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 50;\r\ns_correct = [493074 400112 10866];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = [616091 125112 60156] ;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 111;\r\ns_correct = [135700 562612 77760];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 222;\r\ns_correct = [502853 800112 407761];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 333;\r\ns_correct = [118917 137612 1060631];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 444;\r\ns_correct = [571761 200112 2075648];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\ns1 = []; s2 = [0 0 0];\r\nfor n = 401:450\r\n    s = S(n);\r\n    s1 = [s1 sum(s)];\r\n    s2 = s2 + s;\r\nend\r\ns1_correct = [3399227 2462755 2513309 2591563 2945479 2629800 2429946 2004548 2424123 ... \r\n              2821874 2678061 3274455 2940458 2534820 2560707 3108793 2977734 2787069 ... \r\n              2663207 2472829 2131208 2833671 3029902 3318271 2420784 2658659 3118743 ...\r\n              3225127 2317337 2461778 2482161 2841696 2309811 3155290 3027882 3307035 ...\r\n              2592649 2263026 3857175 3256909 3238654 2485976 3765395 2847521 2904752 ...\r\n              2475937 3468958 3034826 2828495 3129026];\r\ns2_correct = [22037407 24793100 94178904];\r\nassert(isequal(s1,s1_correct))\r\nassert(isequal(s2,s2_correct))\r\nassert(isequal(sum(s1),sum(s2_correct)))\r\nassert(isequal(sum(s2),sum(s1_correct)))\r\n%%\r\nn = 500;\r\ns_correct = [221421 175112 2738917];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 555;\r\ns_correct = [146871 37612 3486572];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = [315383 850112 13508037];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assign') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-12-14T11:15:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2022-12-14T11:15:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-12T11:08:08.000Z","updated_at":"2022-12-14T11:15:42.000Z","published_at":"2022-12-13T10:19:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57412-easy-sequences-85-hyperprimorials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eEasy Sequences 85\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, we define the hyperprimorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, as a exponent ladder of primes numbers from the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime down to first prime (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). OEIS, however, defines hyperprimorial differently. In OEIS sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A076265\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#A076265,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe hyperprimorial of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n=\\\\prod_{i=1}^n p_i^{p_{i}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                             where: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUsing the above formula, we want to calculate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is the sum of all hyperprimorials from 1 to n:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n = \\\\sum_{i=1}^{n} H_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_5 = \\\\sum_{i=1}^{5} H_5=\\\\prod_{i=1}^1 p_i^{p_{i}}+\\\\prod_{i=1}^2 p_i^{p_{i}}+\\\\prod_{i=1}^3 p_i^{p_{i}}+\\\\prod_{i=1}^4 p_i^{p_{i}}+\\\\prod_{i=1}^5 p_i^{p_{i}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e=2^2+(2^2\\\\cdot3^3)+(2^2\\\\cdot3^3\\\\cdot5^5)+(2^2\\\\cdot3^3\\\\cdot5^5\\\\cdot7^7)+(2^2\\\\cdot3^3\\\\cdot5^5\\\\cdot7^7\\\\cdot11^{11})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e=79301169838401181987612\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince this will involve large integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplease output a vector containing first 6, last 6, and the number of digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, the final function output should be:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_n=[793011 \\\\ 987612 \\\\ 23] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57512,"title":"Easy Sequences 89: Double Summation of a Trigonometric Product","description":"Given and angle  in radians and a positive integer , evaluate the following product summation:\r\n                    \r\nwhich 'directly' translates to Matlab as:\r\n    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nFor example  and :\r\n    \u003e\u003e x = 3; A = 1;\r\n    \u003e\u003e PS(A,x)\r\n    ans =\r\n        8.9683\r\nPlease present your answer rounded-off to nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 492.078125px 144px; transform-origin: 492.078125px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven and angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e in radians and a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the following product summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"236\" height=\"46\" style=\"width: 236px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich 'directly' translates to Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 40px; transform-origin: 489.078125px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; x = 3; A = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS(A,x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        8.9683\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = PS(A,x)\r\n    p = sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nend","test_suite":"%%\r\nA = 1; x = 3;\r\np_correct = 8.9683;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2:2:20; x = 3:3:30;\r\np_correct = [1.8697 -3.3674 -62.4997 11.5088 -4.8523 -71.5196 25.1022 -3.2420 -64.7730 49.3233];\r\nassert(isequal(arrayfun(@(i) PS(A(i),x(i)),1:10),p_correct))\r\n%%\r\np_correct = 4166.0746;\r\nassert(isequal(sum(arrayfun(@(i) PS(i,i),1:100)),p_correct))\r\n%%\r\nA = 100; x = 200;\r\np_correct = -739.8950;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2000; x = 3000;\r\np_correct = 2041.1906;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 10000; x = 20000;\r\np_correct = -3131.6478;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 200000; x = 300000;\r\np_correct = -8386548.7261;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 1000000; x = 2000000;\r\np_correct = -11067350.2876;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 123456; xs = 200001:200100;\r\nps = arrayfun(@(x) PS(A,x),xs);\r\nss_correct = [-88558 -88558 -88580 12]; \r\nassert(isequal(floor([mean(ps) median(ps) mode(ps) std(ps)]),ss_correct))\r\n%%\r\nfiletext = fileread('PS.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T06:37:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-06T09:42:25.000Z","updated_at":"2025-11-22T20:00:54.000Z","published_at":"2023-01-07T06:37:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven and angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in radians and a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the following product summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ePS(A,x) = \\\\sum_{n=1}^{x} \\\\sum_{m=1}^{n} \\\\prod_{k=0}^{m-1} 2 \\\\sin \\\\left( \\\\frac_{k\\\\pi}^{m} +A \\\\right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich 'directly' translates to Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e x = 3; A = 1;\\n    \u003e\u003e PS(A,x)\\n    ans =\\n        8.9683]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57954,"title":"Easy Sequences 108: Enclosing a Circle with Primitive Pythagorean Triangles","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and . \r\nWe say that pythagorean triangle is a primitive pythagorean triangle (PPT), if all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are a, b and c, it is PPT if and only if: gcd(a,b) == 1 \u0026\u0026 gcd(a,c) == 1 \u0026\u0026 gcd(b,c) == 1.\r\nGiven a circle of radius R, find the dimensions of the PPT with the smallest area, that can enclose the circle, without touching the circle (i.e. no sides is a tangent of the circle, or crosses the circle). For example, in the figure below, if R = 12, the smallest pythagorean triangle that can enclose the circle without touching it is [39,52,65]. However this is not primitive since, gcd(39,52) = 13 ≠ 1. The correct smallest PPT is the triangle with dimensions: [48 55 73].\r\n                                                   \r\n-----------------------\r\nNOTE:   There can be more than one PPT with smallest area for the same value of R. For example if R = 4.5, there are two possible smallest area PPT: [20 21 29] and [12 35 37]. Both have an area of 210. In cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter. So, for R = 4.5, the function output should be: [20 21 29].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 547px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 273.5px; transform-origin: 407px 273.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePythagorean Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a right triangle all sides of which are represented by integers. Examples are triangles with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGQAAAAmCAYAAAAycj4zAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAZKADAAQAAAABAAAAJgAAAAANiNVoAAAE9ElEQVRoBe2YfYgXRRjHr1fpxCsxxZc6NV+TREpRIjvhKuKMIMsKxCSow0JICat/igzFSML8QzI4/5Go6Ao1CklBKZUsSwvier87KnxLlEOtLkzr87WdY357u7O/2935XcftA5/fzD4z8zzze56dmd2tqiqkiEARgSICRQSKCKSLwEUxw25C/1ZM25voX4hpK9SlEWjisq5U1XVVT+1Q11VQuTSsCK6voJwIX8DRQGeKDlMpysQItNBjeKjXaK6ngmLcTeJWyC303AvzYGu3UdGK2ahnwiRQ5vfBp3AaKiVX42gNtMEqT05HYndUhG3FchbMhYaIdqNaTOU1mAA/GWVSqYT8A/ckdaRdk/sA1D+MEnMDVEp082gOn3h0qBst/D/t6yUJvpUQ9R+f0K+kudyEVDPqS5CDA/BOUNoTPInuKvAtjTgwfn0l5FbLh/Fll6doH5TwR50JiTtDEmx2Na+mNhkehOYubVXVWOpaNVNgMOgA2wy+RMv/FV/GLbtPU/8b1sA5S2+q26h42aLLWSE1gXOdM1FyP0pz97wc1SEnnW6qz6AdOkE+fawQ3Vzn4XXIIs4VcnEGy9cxdh1sibFxzNL/bNXzrj6PwRmwCLRl+JLlGNbB/V5Q+vITabecFRI50FI+S113q5b29ZY+z6rmqS3kxcDob5Q+VoierP4KbMv+CXgfHoKB0BNxrpA4Q1kTchmGD4ImvwJ8iA5PPd7Kj/xJfCXkJWzrv0RxEv0CKFecCcmyZcVNoJoGLesbYUUARe6yHosjYCGczd16qUElej+cKVVfuBrM7xvwXERbbqo0K0TJbQCzMnQ3aU9/AvIW88AQtu1rhZj56wypBZ1X7RBeMfeiSxLnCokb3NOEaFW0QniC5nppnKMU+msYo21iByhAtvhOiO1rABd6DLbPlu+4Ttp1KpIQTVTbhw7vu2EnmGSo7IChkFWUANnWoaqDNiyVTIjx/TgV+7/ONg0xpTMhSdmMsRmpPoL2W9DTx+2giZo990rqd0BWeRID9fAYHM5qLKfxG7DTbNkabdV7XNVLlQ/RHaMPaGPgGZDojT6LaLy+DHwPOpvuhLDoyUuiTzWm/Q/qe6T0KO9i+4HA/rAsfnwlxMzpQyomIXoaySJKyOUwCWTXJdo6TR89Go9zdc6hTQ8yRrQ9pxbfCdEnjPOgrfHH1LP8b6BWnWy5xN6CTd9zrgE5tXVadrR1pxb7D6Q24hiorcP4+NrRr5wmvdtcksDxwNA+q9/EQOezmBYY1+r4OIsjE6wsNlxj7woav6L8yNWxj7fpYUOyCf68UEv5kyUhQ/C5EfT1c1aEfz3mrgRtGU+Btpy+KPos0g4tsATCMWtEdxvoYWM1eJFyXgwfwbOCbPZ2fT7Q0tX7wXz4BbS33geVEh/vIZuZvPmfKrUd1sF0WAvS/QBR70Wou8liNBozvluLQ1FOQmoY/yvYk1Vdh2krvAp6q66k6CbQHHbl6HQmtg4FdsP/VfplUA3lijMhWZ6y9C4wAebAKNDW9E3A75S9IbUenO7H5hi4Ga4FBV83Yju0wVnITbIkRJPQlrQ9t9n8fw0p6LsrMb3wAVUJn4UPRwSKhDiC0xtNSVvWw0wq/PXyc3Rv98Zk+6DPR5lz+BteXZr/MYNB4ScKc92UxmA/HbPFEcex/TQmxd8uIlBEoIhAEYEiAv0jAv8CgUAwjj+ULvgAAAAASUVORK5CYII=\" width=\"50\" height=\"19\" style=\"width: 50px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"19\" style=\"width: 65px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe say that pythagorean triangle is a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eprimitive pythagorean triangle (PPT), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, it is PPT if and only if: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a circle of radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the dimensions of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, in the figure below, if\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e R = 12\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[39,52,65]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. However this is not primitive since, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(39,52) = 13 ≠ 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[48 55 73]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104px; text-align: left; transform-origin: 384px 104px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                   \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"354\" height=\"202\" style=\"vertical-align: baseline;width: 354px;height: 202px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-----------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e There can be more than one PPT with smallest area for the same value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, there are two possible smallest area PPT: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[12 35 37]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Both have an area of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e210\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e So, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the function output should be: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ts = minPPTs(R)\r\n  y = x;\r\nend","test_suite":"%%\r\nR = [4.5, 12];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[20 21 29] [48 55 73]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = 50;\r\nTs_correct = [160 231 281];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 100;\r\nTs_correct = [336 377 505];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 200:50:800;\r\nPs = arrayfun(@(r) sum(minPPTs(r)),R)\r\nPs_correct = [2378 3008 3570 4240 4902 5368 6030 6432 7100 7592 8374 8848 9396];\r\nassert(isequal(Ps,Ps_correct))\r\n%%\r\nR = 900;\r\nTs_correct = [3045 3172 4397];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 1000;\r\nTs_correct = [3255 3712 4937];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = [123 1234 12345 123456];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[429 460 629] [4176 4343 6025] [42036 42427 59725] [417543 425776 596345]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = randi([100000,1000000])\r\nTs = minPPTs(R);\r\nr = prod(Ts(1:2)) / sum(Ts)\r\nassert(gcd(Ts(1),Ts(2))==1)\r\nassert(isequal(sqrt(sum(Ts(1:2).^2)),Ts(3)))\r\nassert((r\u003eR) \u0026\u0026 ((r-R)/R\u003c0.0005))\r\n%%\r\nR = 1000000;\r\nTs_correct = [3404505 3424952 4829177];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nfiletext = fileread('minPPTs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-12T18:05:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T11:52:42.000Z","updated_at":"2023-04-12T18:05:02.000Z","published_at":"2023-04-12T18:05:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePythagorean Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a right triangle all sides of which are represented by integers. Examples are triangles with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3\\\\ 4\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe say that pythagorean triangle is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprimitive pythagorean triangle (PPT), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, it is PPT if and only if: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a circle of radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the dimensions of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the figure below, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e R = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[39,52,65]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However this is not primitive since, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(39,52) = 13 ≠ 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[48 55 73]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"202\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"354\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-----------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There can be more than one PPT with smallest area for the same value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there are two possible smallest area PPT: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[12 35 37]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Both have an area of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e So, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function output should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMwMgAAkpIAAgAAAAMwMgAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Sequences 91: Generalized McCarthy-91 Recursive Function","description":"The McCarthy 91 function is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\r\nThe McCarthy 91 function is defined for integer  as: \r\n                                        \r\nRemarkably, the function yields  for all  (hence, the function name).\r\nA more generalized form of the McCarthy's recursive function is defined below: \r\n                                        \r\nFor positive integers , , , , and . \r\nThe expression , means applying the function ,  number of times:\r\n                                        \r\nThis means that the 'original' McCarthy-91 function  is actually , with , ,  and .\r\nGiven integers, , , , , and , evaluate the value of .\r\n--------------------\r\nNOTE: The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 454px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 227px; transform-origin: 407px 227px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/McCarthy_91_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMcCarthy 91 function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 286.5px 8px; transform-origin: 286.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167.5px 8px; transform-origin: 167.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe McCarthy 91 function is defined for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e as:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 366.5px; height: 18.5px;\" width=\"366.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemarkably, the function yields \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 70.5px; height: 18.5px;\" width=\"70.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 51.5px; height: 18px;\" width=\"51.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89px 8px; transform-origin: 89px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (hence, the function name).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 280px 8px; transform-origin: 280px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA more generalized form of the McCarthy's recursive function is defined below: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 291px; height: 19.5px;\" width=\"291\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5px 8px; transform-origin: 66.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe expression \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 61px; height: 19.5px;\" width=\"61\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, means applying the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eG\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number of times:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 52px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 26px; text-align: left; transform-origin: 384px 26px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 165px; height: 52px;\" width=\"165\" height=\"52\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis means that the 'original' McCarthy-91 function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 37px; height: 18.5px;\" width=\"37\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is actually \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 51.5px; height: 18px;\" width=\"51.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 43.5px; height: 18px;\" width=\"43.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36px; height: 18px;\" width=\"36\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = M(a,b,c,k,n)\r\n    m = G(n);\r\n    function g = G(x)\r\n        if x \u003e a\r\n            g = x - b;\r\n        else\r\n            g = G(G(G(G(x+c)))); % k-times\r\n        end\r\n    end\r\nend","test_suite":"%%\r\na = 100; b = 10; c = 11; k = 2; n = [1:20 201:220];\r\nm_correct = [repelem(91,20) 191:210];\r\nassert(isequal(arrayfun(@(i) M(a,b,c,k,i),n),m_correct))\r\n%%\r\na = 333; b = 3; c = 33; k = 3; n = 33;\r\nm_correct = 354;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 4444; b = 444; c = 444; k = 4; n = 444444;\r\nm_correct = 444000;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 55555; b = 555; c = 5555; k = 5; n = 5;\r\nm_correct = 56145;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 7777777; b = 77777; c = 777777; k = 7; n = 777;\r\nm_correct = 7700875;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 999999999; b = 9999; c = 999999; k = 99; n = 999;\r\nm_correct = 999997623;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 9999999999; b = 9; c = 99999999; k = 99999; n = 9999;\r\nm_correct = 10009111707;\r\nassert(isequal(M(a,b,c,k,n),m_correct))\r\n%%\r\na = 7654321; b = 891011; c = 171615141312; k = 181920; n = 1:100;\r\ns_correct = 952242024250;\r\nassert(isequal(sum(arrayfun(@(i) M(a,b,c,k,i),n)),s_correct))\r\n%%\r\na = 10000000000; b = 1000000; c = 1000000000000; k = 1000000; n = 1:1000;\r\nm = arrayfun(@(i) M(a,b,c,k,i),n);\r\ns_correct = [9999000500 9999000500 9999000001 288];\r\nassert(isequal(floor([mean(m) median(m) mode(m) std(m)]),s_correct))\r\n%%\r\nfiletext = fileread('M.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-19T04:00:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-17T23:39:34.000Z","updated_at":"2025-08-23T09:20:38.000Z","published_at":"2023-01-18T08:07:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/McCarthy_91_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMcCarthy 91 function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe McCarthy 91 function is defined for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e as:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n) = n-10 \\\\ \\\\text{if} \\\\ n \u0026gt; 100 \\\\ \\\\text{and} \\\\ \\nM(M(n+11))  \\\\ \\\\text{if} \\\\ n \\\\le 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarkably, the function yields \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n) = 91\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\le 101\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (hence, the function name).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA more generalized form of the McCarthy's recursive function is defined below: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n) = n-b \\\\ \\\\text{if} \\\\ n \u0026gt; a \\\\ \\\\text{and} \\\\ \\nG^k(n+c)  \\\\ \\\\text{if} \\\\ n \\\\le a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe expression \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG^k(n+c) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, means applying the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e number of times:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG^k(x) = \\\\underbrace{G(G(G(...G(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{k times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis means that the 'original' McCarthy-91 function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is actually \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec=11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The McCarthy-91 function was created to test recursive function implementations. In this problem, while iterative loops are allowed, use of recursion is encouraged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57565,"title":"Easy Sequences 92: Number of Roots of a System of Linear Diophantine Equations","description":"One of the tasks that Matlab is very good at, is in solving systems of linear equations. \r\nIn this problem we shall tackle a system of linear Diophantine Equations in which the roots are limited to certain range.\r\nGiven the number of variables , positive integers, ,  and a root limit, , create the function, numRoots(n,a,b,L), that outputs the number of posible integer root sets of the following system of equations:\r\n                \r\n                \r\n        with:\r\n                .\r\nFor example, if , the system of equations:  and , where , has only one root set, namely: . Therefore, numRoots(2,10,4,1) = 1.\r\nIf , two of the possible roots of:\r\n                ; and\r\n                \r\n                where:  \r\nare and . In fact, there are  possible root sets. Therefore, numRoots(4,20,6,3) = 16.\r\nThere are no possible roots for  and , therefore in these cases the function should return: numRoots = 0.\r\n-------------------------\r\nNOTE: As an added challenge, only those solutions with Cody program size of less than or equal to 200 will be accepted.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 607.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 303.75px; transform-origin: 407px 303.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 270px 8px; transform-origin: 270px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the tasks that Matlab is very good at, is in solving systems of linear equations. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem we shall tackle a system of linear \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Diophantine_equation\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDiophantine Equations\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145.5px 8px; transform-origin: 145.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in which the roots are limited to certain range.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the number of variables \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epositive integers, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a root limit, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, create the function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 68px 8.5px; transform-origin: 68px 8.5px; \"\u003enumRoots(n,a,b,L)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 281px 8px; transform-origin: 281px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that outputs the number of posible integer root sets of the following system of equations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 249.5px; height: 20px;\" width=\"249.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"width: 378.5px; height: 21px;\" width=\"378.5\" height=\"21\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e        with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 132.5px; height: 20px;\" width=\"132.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83px 8px; transform-origin: 83px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the system of equations: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJoAAAAoCAYAAAAG/eNpAAAFtElEQVR4Xu2bScsdRRSGkx/gFF25EHFYiAuFOIDoRnBAQQgRNAoSUNAouHMWXDhnIwSiiWtDdCtxiC4EJ3CCCIILB0TElSP+AH0f7SPnq1vVXXVvd3/d362Gd3G7azqn3jp1zqm627fVp2pgBA1sH6GP2kXVwLZKtEqCUTRQiTaKmmsnlWiVA6NooBJtFDXXTirRKgfQwEXCl4WqoM5Jwl85dSvRCrW7xYpfKXkeFy4TdmTIdrrK3Ck8LLwk/ClcLZwn3C+8mWqjEi1Du1uwCNboeeG6RrbfM4gGyd4WLhFuDEj1qn7fIjwjPBbTVyXaFmRRh0h36/spwlfCK8JpQg7RjEyvqfytQR+Q8JumrZCE/xadE9FYTazAe4TD68ePQSQ2nXYRjS32g2YEUSLp24vCPuE74XLhVz/iSrRB5m82jeYSzawZhGTr/D4iIVbuaIqMlWiz4cQgA80hGtviL03vWCsc/9iD33ei+UCgcG+pRcNsxkLYc/T+TOHr0EwOopL/HNGhtk4L1T8Mxo6SLxB+TqzigUQdrdkcovltM+af+cH+nSJkyqLhMO5qJpa6ocl8Wu8ebRpNRho9q6tvot2g8d0hXCvgEPN4/4OtAL+Db8eF23tcUEbsVVUULozS9nKIBhcONQ3nEo3iZ3h9pYhmCTy/75oTDsmYnM8EnL+xnPO+iWYyYpnZEnhMkZCQiIwtABnfEcJIq3RSfXmTZZU2uhz4nLZziPagGiIV4vWTatssGt8vFv5PAuf4aFYZpR8TDgipfTpHuGXL9E202MR/rpd3Ce8JKad32fH7eizWnSs29EcP5C8lWpdR8QuomGhWmVVP9vh8YUPouqLCrLr5fKnmXmgmn636rZY+l/EZ/aqFbE8IySx3T/JOoZlSoj2kQe9vGTi7HAuUp5hofhK6GL2K8nw/q7SzQcDMhkoc3swmZ1GslGglPlox0XKSdV6rdrzxhV5GjyMSU4APtLdlejiPwzHHsn7bUo6wOpbn6Zp5cxHaghui0CcFfNRzBfyk5zpWeVe/m/k9h2gli9B0uOA/5vhoPj/SZjrZ+m4WOHCFEH1Ho0P6aBDok4Y8RJjXR2bfzvoIDNi6LxSebWRN1UmRaE5RZyxYSsllRMP9uNQX6iKanwDqLTTgGmNAnOZzuk+UMieiWebbxNkQmjcvCfPPEryV9ouwZMueU9SJ+OwgZsFTtzy85VuY+y6iMQG/CT805KHT2CR48pqvNReiQaAHhL1C23keuiB3GG7L5gCnzgBjq39OUSfj9/4zhIu5Jj7ftrDo2ohGRUJ9TGDMT+PdFUIYhcyJaGaRbPGEfhoW/aDQlkMz61Ri0WLk24x3OT4a4/K3M1Luky24aMDgiYbSOeLh+sjJAllxn8rw+TRuT5BriqU6pkw0u7j3o8b+k/C6cJNgGXZTPC4C96tQWleqwwKThRsLm8Gcwj5ziUazJLHfEGK3M8wQ8Y1AacHieaKFfkO4QkM/JrWCp0y0MIUSpmu8+Ue5Xekcc5T3qCz6mdPjdynGfZVbcCk57KSI4Meie9phweJi7RaiV8I90WAs13HJOBNNhRWweI80I4h9t8FNmWgmw6kaLCccYVLW0hcQKPY9nACsPs7xfcIQSewhiAsxbhOQMXxISX0U0YsvZ9kFrnDzYL3eF95t00FXMLCMoEMRjdVE1PexsOph8jJyhXWYME4r2GKXydv1MYbZtDEnok1Jqaxq8mlRf2RKA53KWCrRymeC7fWI8NRELGu5BJtQoxKtTOl2OhCLRHEZcJJL/x9ZNoKZlh6CaHYpsu+E7RRUTK6I47WXg8Gcrd9sp31ejpyCvL2NoU+ioehrBDv/42CVEPjTLeIs2798UsrvSoX0NmlzbKhPos1R/jrmkTRQiTaSote9m0q0dWfASPJXoo2k6HXvphJt3RkwkvyVaCMpet27qURbdwaMJP8/YupiOGKJgUwAAAAASUVORK5CYII=\" style=\"width: 77px; height: 20px;\" width=\"77\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 69.5px; height: 20px;\" width=\"69.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 58.5px; height: 20px;\" width=\"58.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, has only one root set, namely: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 96px; height: 20px;\" width=\"96\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; \"\u003enumRoots(2,10,4,1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.5px 8px; transform-origin: 90.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, two of the possible roots of:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 134px; height: 20px;\" width=\"134\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 126.5px; height: 20px;\" width=\"126.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                where:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 94.5px; height: 20px;\" width=\"94.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.75px; text-align: left; transform-origin: 384px 21.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eare \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"width: 166.5px; height: 20px;\" width=\"166.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In fact, there are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e possible root sets. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; \"\u003enumRoots(4,20,6,3)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e=\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6px 8px; transform-origin: 6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are no possible roots for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 185px; height: 18.5px;\" width=\"185\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 175px; height: 18.5px;\" width=\"175\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore in these cases the function should return: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 48px 8.5px; transform-origin: 48px 8.5px; \"\u003enumRoots = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.5px 8px; transform-origin: 62.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs an added challenge, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eonly those solutions with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/content/cody/about.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eCody program size\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85px 8px; transform-origin: 85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003e200\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e will be accepted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = numRoots(n,a,b,L)\r\n    n = 'number of unknown variables';\r\n    a = 'sum of the unknown variables';\r\n    b = 'alternating sum and difference of the unknown variables';\r\n    L = 'limit of the roots (i.e. all roots should be \u003e L');\r\n    c = 'the number of root sets';\r\nend","test_suite":"%%\r\n[n,a,b,L] = deal(4,20,6,3);\r\nc_correct = 16;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(4,20,6,-3);\r\nc_correct = 280;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(3,20,6,4);\r\nc_correct = 6;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n%%\r\n[n,a,b,L] = deal(2,10,4,1);\r\nc_correct = 1;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(10,55,10,-10);\r\nc_correct = 0;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n[n,a,b,L] = deal(42,10,2,100);\r\nc_correct = 0;\r\nassert(isequal(str2num(numRoots(n,a,b,L)),c_correct))\r\n%%\r\n[n,a,b,L] = deal(10,25,15,-5);\r\nc_correct = '9825961376';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(25,50,25,5);\r\nc_correct = '0';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(8,88,8,8);\r\nc_correct = '159885';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(88,88,8,8);\r\nc_correct = '0';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n[n,a,b,L] = deal(8,888,88,-8);\r\nc_correct =  '322979008681245';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(11,111,11,-1);\r\nc_correct =  '6367915454544';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(111,11111,111,11);\r\nc_correct = '2909165067998259047855867968538898760414304923603195356244648530663146995238036844997557527483252003388541616691119031429859046897494224647322949977583143171656492664325583077702371945252381217441222592230772490362933347417600378555600078275316289441596896000';\r\nassert(isequal(numRoots(n,a,b,L),c_correct))\r\n%%\r\n[n,a,b,L] = deal(1234,56789,1011,12);\r\nc = numRoots(n,a,b,L);\r\ns = [sum(c) histc(c,50:55) sum(c\u003c58) sum(c\u003e47)]\r\ns_correct = [127146 260 249 257 231 226 247 2428 2428];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('numRoots.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)\r\nassert(mtree(filetext).count\u003c=150)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-07T05:06:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-18T14:33:46.000Z","updated_at":"2023-02-07T05:06:35.000Z","published_at":"2023-02-02T11:44:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the tasks that Matlab is very good at, is in solving systems of linear equations. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem we shall tackle a system of linear \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Diophantine_equation\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDiophantine Equations\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in which the roots are limited to certain range.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the number of variables \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epositive integers, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a root limit, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, create the function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(n,a,b,L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that outputs the number of posible integer root sets of the following system of equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2+x_3+x_4...+x_{n-2}+x_{n-1}+x_n=a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2+x_3-x_4...+(-1)^{n-1}x_{n-2}+(-1)^{n}x_{n-1}+(-1)^{n+1}x_n=b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e        with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2,x_3...x_{n-1},x_n \\\\ge L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (2,10,4,1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the system of equations: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2\\\\ge 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, has only one root set, namely: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2)=(7,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(2,10,4,1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (4,20,6,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, two of the possible roots of:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1+x_2+x_3+x_4=20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1-x_2+x_3-x_4=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1,x_2,x_3,x_4 \\\\ge 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eare \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2,x_3,x_4)=(5,4,8,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_1,x_2,x_3,x_4)=(10,3,3,4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In fact, there are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e possible root sets. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots(4,20,6,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e=\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are no possible roots for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (10,55,10,-10)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,a,b,L) = (42,10,2,100)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore in these cases the function should return: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumRoots = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eAs an added challenge, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly those solutions with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/content/cody/about.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody program size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e200\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e will be accepted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57745,"title":"Easy Sequences 100: One-line Code Challenge - 100th Digit of 100th power of an Integer","description":"Given a integer , write a function that computes the  digit of . If  has less than  digits just output a NaN.\r\nFor example if , the function should output: . \r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nPlease suppress the function end line. Keyword 'end' is not allowed.\r\nImporting libraries is not allowed.\r\nRegular expressions, base conversion and string manipulation are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 245.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 122.833px; transform-origin: 407px 122.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126px 8px; transform-origin: 126px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that computes the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33.5px; height: 19px;\" width=\"33.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e digit of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 19px;\" width=\"25.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 19px;\" width=\"25.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.5px 8px; transform-origin: 55.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits just output a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 100px; height: 18.5px;\" width=\"100\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the function should output: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 78px; height: 18.5px;\" width=\"78\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 103.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.5833px; transform-origin: 391px 51.5833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.9333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.4667px; text-align: left; transform-origin: 363px 10.4667px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease suppress the function end line. Keyword '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\u003eend'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.5px 8px; transform-origin: 46.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 102.5px 8px; transform-origin: 102.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImporting libraries is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 248px 8px; transform-origin: 248px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, base conversion and string manipulation are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = digpow100(n)\r\n    import java.math.BigInteger\r\n    s = arrayfun(@(a) char(BigInteger(num2str(a)).pow(100)),n,'uni',0);\r\n    d = cellfun(@(a) str2num(a(100)),s);","test_suite":"%%\r\nn = 25;\r\nd_correct = 6;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 1:20;\r\nd_correct = [repelem(NaN,9) 0 4 3 0 1 1 1 3 8 4 0];\r\nassert(isequaln(digpow100(n),d_correct))\r\n%%\r\nn = 41:50;\r\nd_correct = [4 1 0 6 1 1 1 6 5 0];\r\nassert(isequaln(digpow100(n),d_correct))\r\n%%\r\nn = [111 222 333 444 555];\r\nd_correct = [0 2 3 3 6];\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 12345;\r\nd_correct = 8;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nn = 123456789;\r\nd_correct = 0;\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nimport java.math.BigInteger\r\nn = randi(10000,1,10)\r\nf = @(a) char(BigInteger(num2str(a)).pow(100));\r\nd_correct = [];\r\nfor a = n\r\n    if a \u003c 10\r\n        d_correct = [d_correct NaN];\r\n    else\r\n        b = f(a);\r\n        d_correct = [d_correct str2num(b(100))];\r\n    end\r\nend\r\nassert(isequal(digpow100(n),d_correct))\r\n%%\r\nfiletext = fileread('digpow100.m');\r\nnot_allowed = contains(filetext, 'import') || contains(filetext, 'str2') || contains(filetext, 'num2') || contains(filetext, 'dec2') || contains(filetext, 'base2') || contains(filetext, 'sprintf') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'end');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-06T03:48:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-03T04:05:24.000Z","updated_at":"2023-03-06T03:48:34.000Z","published_at":"2023-03-05T17:27:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that computes the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100^{\\\\text{th}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e digit of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^{100}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e has less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits just output a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = [9,\\\\ 10,\\\\ 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should output: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[\\\\text{NaN},\\\\ 0,\\\\ 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease suppress the function end line. Keyword '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eend'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImporting libraries is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, base conversion and string manipulation are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57730,"title":"Easy Sequences 97: One-line Code Challenge - Sequence with Constant Difference","description":"While answering Problem #57725, I noticed a pattern that immediately led me to a solution, namely: the -th difference of the sequence is constant. In that problem's case the constant is 6:\r\n    diff(A,4) == [6 6 6 6 ...]\r\nwhere  is the sequence.\r\nGiven an integer  and a vector  that enumerates the first  elements of , write a function that outputs the -th element of , such that the -th difference is a constant:\r\n    diff(A,k-1) == [c c c c ...]\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nTo encourage vectorization, for and while loops are not allowed\r\nRegular expressions, string manipulation and curve fitting are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 335px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 167.5px; transform-origin: 407px 167.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhile answering \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57725\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem #57725\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    diff(A,4) == [6 6 6 6 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e that enumerates the first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e elements of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that outputs the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th difference is a constant:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    diff(A,k-1) == [c c c c \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40px; transform-origin: 391px 40px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewhile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eloops are not allowed\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = nthElement(V,n)\r\n    x = A(n);\r\nend","test_suite":"format longg\r\n%%\r\nV = [1 2 3 4 5 6]; n = 10000;\r\nx_correct = n;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [790 1303 2033 3034 4366]; n = [10 100 1000];\r\nx_correct = [18511 32160346 256563524446];\r\nassert(isequal(arrayfun(@(i) nthElement(V,i),n),x_correct))\r\n%%\r\nV = [12 23 34 56 78]; n = 6:10;\r\nds = diff([V arrayfun(@(i) nthElement(V,i),n)],length(V)-1);\r\nd_correct = -22;\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = [123456 234567 345678 456789]; n = 10000;\r\nx_correct = 1111122346;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [123 456 789 101112 131415 161718 192021 222324 252627 282930]; n = 11:18;\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\ns_correct = sum(x)\r\nds = diff([V x],length(V)-1);\r\nd_correct = 2170350;\r\nassert(isequal(sum(x),s_correct))\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = sort(randi(100,1,10)); n = (length(V)+1):(length(V)+20);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(~any(diff([V x],length(V))))\r\n%%\r\nV = sort(randi(1000,1,10)); n = (length(V)+1):(length(V)+10);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(isequal(diff(V,length(V)-1),diff(x,length(V)-1)))\r\n%%\r\nfiletext = fileread('nthElement.m');\r\nnot_allowed = contains(filetext, 'str') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'fit');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-25T18:40:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-25T12:35:50.000Z","updated_at":"2023-02-25T18:40:33.000Z","published_at":"2023-02-25T18:35:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile answering \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57725\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem #57725\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    diff(A,4) == [6 6 6 6 ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e that enumerates the first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e elements of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that outputs the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th difference is a constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    diff(A,k-1) == [c c c c ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eloops are not allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55500,"title":"Easy Sequences 71:  A Nonlinear Function with Quadratic Domain","description":"Consider the function:\r\n                     \r\nThe outputs of this function are fed as domain to another function:\r\n                    \r\nwhere , is the Gamma Function.\r\nGiven the values of , , , and a limit , find the all values of, so that  and . For example if , and , the only integer values of  that will satisfy the above criteria are:\r\n                    . \r\nPlease present the final output as a unique row vector sorted ascending. \r\n-----------------\r\nNOTE: Some MATLAB's built-in math functions may only give approximate values. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 347.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 173.75px; transform-origin: 343px 173.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.75px; text-align: left; transform-origin: 320px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"104\" height=\"19.5\" style=\"width: 104px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe outputs of this function are fed as domain to another function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"153.5\" height=\"35\" style=\"width: 153.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31\" height=\"18\" style=\"width: 31px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gamma_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGamma Function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 31.5px; text-align: left; transform-origin: 320px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, and a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e find the all values of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, so that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"18\" style=\"width: 35px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37\" height=\"18\" style=\"width: 37px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112\" height=\"18\" style=\"width: 112px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the only integer values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that will satisfy the above criteria are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"266\" height=\"18\" style=\"width: 266px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output as a unique row vector sorted ascending. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-----------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Some MATLAB's built-in math functions may only give approximate values. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xs = intXs(a,b,c,n)\r\n  xs = a + b + c;\r\nend","test_suite":"%%\r\na = 1; b = 1; c = 1; \r\nn = 50;\r\nxs_correct = [-7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 6];\r\nassert(isequal(intXs(a,b,c,n),xs_correct))\r\n%%\r\na = 1; b = 2; c = 1;\r\nn = 500;\r\nxs = intXs(a,b,c,n);\r\nss_correct = -1;\r\nassert(isequal(mean(xs),ss_correct))\r\n%%\r\nas = 1:25; bs = -(101:-3:1); cs = primes(100);\r\nn = 1e4;\r\nxs = unique(arrayfun(@(i) sum(intXs(as(i),bs(i),cs(i),n)),1:25))\r\nxs_correct = [-13 -10 -8 -4 -3 2 4 7 11 16 19 49 52 55 67 73 93 101 114 125 204 270 294 345 614];\r\nassert(isequal(xs,xs_correct))\r\n%%\r\na = 10; b = 2; c = 101;\r\nn = 12345;\r\nxs_correct = [-35 -34 -31 -30 -25 -24 -19 -17 -11 -7 -6 -2 -1 0 1 3 4 8 9 14 15 16 23 30 33];\r\nassert(isequal(intXs(a,b,c,n),xs_correct))\r\n%%\r\na = 11; b = -31; c = 41;\r\nn = 1e6;\r\nxs = intXs(a,b,c,n);\r\nss_correct = [313 1165 130];\r\nassert(isequal([sum(xs(2:2:end)) sum(abs(xs(11:11:end))) floor(mean(abs(xs)))],ss_correct))\r\n%%\r\na = 131; b = -117; c = 119;\r\nn = 1e7;\r\nxs = intXs(a,b,c,n);\r\nss_correct = [13473 148];\r\nassert(isequal(floor([sum(abs(xs)) std(xs)]),ss_correct))\r\n%%\r\na = 13; b = -17; c = -19;\r\nn = double(intmax);\r\nxs = intXs(a,b,c,n);\r\nss_correct = [9102 9119 9142 9160 9193 9225 3 -14169663];\r\nassert(isequal([xs(4000:5:4025) mode(abs(xs)) sum(xs(xs\u003c0))],ss_correct))\r\n%%\r\nfiletext = fileread('intXs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":255988,"edited_by":255988,"edited_at":"2022-09-07T15:09:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2022-09-07T05:56:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-06T07:12:19.000Z","updated_at":"2022-09-07T15:09:06.000Z","published_at":"2022-09-06T19:29:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = ax^2+bx+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe outputs of this function are fed as domain to another function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=\\\\sin\\\\left( \\\\pi\\\\ \\\\cdot\\\\ \\\\frac{\\\\Gamma(y)+1}y{} \\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gamma_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGamma Function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, and a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e find the all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\\\\in\\\\mathrm{Z}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, so that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \\\\le n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[a, b, c]= [1,1,1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the only integer values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that will satisfy the above criteria are:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs=[-7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output as a unique row vector sorted ascending. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-----------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Some MATLAB's built-in math functions may only give approximate values. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52804,"title":"Easy Sequences 29: Odd proper divisors of odd proper divisors","description":"The number  is special. It has odd number of proper divisors:  . Furthermore, if you take any of its proper divisors, say , it too has odd number of proper divisors: . The numbers  and , have similar property as . \r\nGiven a limit , find how many integers , have similar property as 210, namely, the integers should have odd number of proper divisors and all its proper divisors have odd number of proper divisors, as well. \r\nThe number , does not qualify because it has even proper divisors,  in total  . The number  also doesn't qualify because although it has proper divisors, some of its divisor, like , have even number of proper divisors. \r\nNOTE: A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number , which is considered a proper divisor of itself.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 237px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.5px; transform-origin: 407px 118.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155px 8px; transform-origin: 155px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is special. It has odd number of proper divisors:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 288.5px; height: 18.5px;\" width=\"288.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Furthermore, if you take \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eany\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83px 8px; transform-origin: 83px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of its proper divisors, say \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it too has odd number of proper divisors: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPwAAAAlCAYAAABmmoSAAAAF7ElEQVR4nO2cW7UqMQyGfw84GANjAAUowAEOcIAFNCABD1hAAxb2eejOmVB6S5uWzZBvrXk5hz1tk/xtehvAMAzDMAzDMIyVcow823dWyjCM/2wR16mYHwA3AFfv2WvU1DCMZvZ41ecNTrtifmCjuWF8Glu8SfBzw9+Wsv19epe1YWX5zw7ASaGMOVGG//Rsb827qV6Tcl1STHB+qYV82vKOkvdLNdQaa8MFvwdwB3CpKbSADYAzXP348wBw6FTmMVAefzQyoXumDP5odDA+Ur9NcH54YJk33uHSyp4dEpX701gOpb7add2xd/s+K+lcWmNtmOB3eA7aHoKf4AJspBg2mTKvCmXsEu/v1cHwsqV+m+FscsezYDbsXTvFOtK7/Y6+VqxcVJqC32OJiSNcLHLb5mJFI9aGCP4EN7oeIAscKVc4A/KFwxmvgaAZbDRy9Ur9gGXBJZUSb+Dadlcst8ZvXNShjIoC7gd6NtvB+cEfPWunHxqdRui9d4Rjj8dnSlMasTY8pe8l+B1c7xdzEO+1Nct+oE8KTUwoczKNHr3qUmo7svMD8Q6KOoQenX7L6Ewj6KXhHTFSU5mJlZeadmrE2moEf0HaWDQCUjBqQCI7oN+8dEKZnSlIe+2clPqNUs5b4jd8RNPOjFoEf4ETJh/lNfy6QX67Opd9asXaagR/Rn4V+ApdwfsLaY/feozYgeBQZ/ZAv6lFid/4WsM58Ts+RdA+t1Er+AOcP6mD7TGHj0EjfCqT04q11Qi+BBK8xkIa9bix54y+8/pQXVIia6XEb1xsqWyLC0q7zjWCp0VGiufRgqc650Z3jVj7KsGnFpNqoNHggOd5H181HSF6Klt75ZtT4jdug1LBp1L/GmoEf8Pz3Hik4PdwnU3Od1qx9jWC52lTrwMgE16dUXVuWcCIdB4o89sVcsFrTa8IqeBPcILnthsh+BnPsSI9J1Iba18jeAqEXodvODwF6y3EEek8IBd8Tih/QfBbhHd2egv+hGUL2R+ppavw0lj7CsHTdovG3L2UE5a29rxzMCKdB+SCT7W5x44JUSp4ioncWYHeKX1opJaWKYm1rxD8Ba9pW29K91ZbGJXOA+tL6S+It2X0oh3wLFrpNFASa6sXPG23jN4qA5ZTX70EPyqdB8r8VrNKrx0HJYI/YFkoC11C8bcN6d97dqo866mxSWmsrVrwdOHjHWIHlhGv1zcC6P2903mgzG98PlkqeO2TgSWC55mI5OkdR1SvGm2UxtpqBf9usQNLr9tjV4DSuBHpPFDmt6nwd1yU2p1VieBp0Sz28PP4/CMvva/3kmhrMsLSWFul4OmGV0rsM/o6kIJfe5+ZoLRzRDoPlPuNgjZ1iefCfvOXjtYS75jDA84eqTsIMSSx9mcFv4EL6iNkRvdPTcXefcOzYbe/Ze1RFoT0QYoYdF489JvatnGoRy+ZLkjbFqLUb1wssbbH0n4Nu4wSvIZNQ2WGpjgtsRYrR0xvwdfcbSax3xD/eB//EAPBU9GSuvFFnVAmQXPZ2Gpr671tns7nRgNp22JI/p5WnEO/JUGGtkg17rOPELzUpvw7DaEPXVDchk7Ltcaaz1DBc2fkTrz5e5O51JWMVroAs/P+1v//VN38O9NUvyOWAxWpuam0bT4UBCXnCqRtCyHxG0Hi5QHO6x0aFVvtQleJ6e9rTznmBC+1qd9B0DXXI1wb74jP21tjLfY+MRLB77FcPfSfWPo2s7+hm0EpYu8PPRe8BhwZsHTxY8Lr4g+leDmkbfOhcksdLW0bUeM3zhbPNjpl6lxrl5Av6DlDvgg2s7+P2Upq0+1vXXgM0kc7crTEWqgeQ1P6GkZ+/pq+TDKKNbethZF2aeGTbAp8gOBn9P+EFCf3IQ1N1ty2FkbbpYVPsSnxpwU/w6VMo7ZGzuj7uSrOmtvWwmi7tPApNuU0Cf6A12OJWnvbGzhjjvqW+R7jUsg1t62F0XZp4RNsSnfoQ8eGxcRWv3vf/zYMo4zUN+wNwzAMwzAMwzAMwzAMw/gE/gF/Uqdxq8aqHgAAAABJRU5ErkJggg==\" style=\"width: 126px; height: 18.5px;\" width=\"126\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA+klEQVRYhe2WTQ2EMBBGn4c6wAAGVgEKcICDdbAW0FAJeMBCNWBh99CS8NPpEqYQDn3JXAjvS5uZQqFQKDyDV6j6ZneFAXrgu6kJ6C50o1RB3gYu63OBKzIADmgXz2r2u24yu1Ea/A6lnr8XoTajK2JJ99mwnolcrkiPn4MUgxCqcVXMocPNrogLoWeOsMaNUoVAx//25HRF5pNyZocaN4rBD+OZ/mtcEQuMIfxON0qH7/2Zn6TGjdIqAjXu8xfTHAisiR9hjSu+POEvVxIGP6jbUI2bXMyI/3ZI5dgfY42bXEzqgiXdazSuiA0rP1KW9XdF4xYKhUIhxg+zAZ+7e7/gtwAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.5px 8px; transform-origin: 81.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have similar property as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABvElEQVRYhe2XXbGDMBCFPw84wAAGqgAFOMBBHdRCNSABD7WAhlrofUj2NmVIcgLcmTvTnJm8MPt3NptlFyoqKiq+CRd/ugM2WqDZoWO+D6EB7sBrdZ7AWBiQ2VGTMQALMAFXr29+SxNC65XXRMJzy9jYSoZCxnTW9kf/faaQ0IzLzBB86zaC6yP6PS6jPfBAJ2MBL5GAZ7REfgTyTDi+BsFNgr1QPkWm4V0NsWAH0dYvJtJvouHz/eSgkhnJ33iLXuaAK6U2I2PXfSaZsBxT/u32FsG3BCMzC7IqGfW2ZzTSMhZvTGnRCpmOfWRi5SjD6nZBy4xC5sI+MiX/u2RwqqFSMrkOGdo7RMbap/JWtpwrZHK2b5xEZsJ1nZI/8L8ssxH3TkqHzb/sZrsGXxv89iirZKxDqmSe7GjNR4iATuYuypnMozSQnjyRjnSGVDLhuxkiMuH/qOi9dLirTC1GDS5DZ5CB/GRhnSw2VW/CiDx8MLGzJBwbSsiEe9RaNpyq5c3TiKQWM2WnseCWQPZa4D9cQ1reg2jRCDPhsq2cie3rbnElsaVzJ1/vjZexWGwtOWWwrKioqKio+Hr8APdp8s/iNd03AAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.5px 8px; transform-origin: 87.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find how many integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have similar property as 210, namely, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106px 8px; transform-origin: 106px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe integers should have odd number of proper divisors and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eall\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 196.5px 8px; transform-origin: 196.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e its proper divisors have odd number of proper divisors\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29px 8px; transform-origin: 29px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, as well. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 172.5px 8px; transform-origin: 172.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, does not qualify because it has even proper divisors, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e8\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in total  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAScAAAAlCAYAAAAA5S/+AAAGvklEQVR4nO1c7ZHqMAzcHuiABmjgKqACOqADOrgWqIES6IEWqIEWeD/CDsLYjj8kHy9oZzJzwyWxvZLXku0YcDgcDofD4XA4HA7HQnFIXD9/WSmHw/FfQlVP7gAuAM7BtdOoqcPh+CqEOnIGcMMkUNW4w6Mkh8NhhzP+SJw2Hc+W4udxjSgrxMaw3A2ebQuvI4C1Ubksuxasm2W9wrJa6rkWz1tDlrWqeG6FtO23AH51q9ntaz2cDhenHYArgFNLoQVYYSLtHlw3AHujMkNsH2VatHGFqS1h+3idDcoE6u22xmQHhuaHx/Nn6It2r81l2w6i3nvUCUcJto+yYnYrEe9D5Fl5aQprj69pcDpMnEKjWHTcNfJk3qE/soSQBrVo40jnBNrstsHEwRWvQrQS79oq1a/X5sfEPXs8O6CWQP3O1POGvECNHphafU2L0yHi9PuoGCtn1XHPmJxfTspv8D6qanWMVB2s2kjnHBUBtthNClCsnj/iXRqdvsfmbNc1URfaUmNAY7tlKrTCM8JgPS+ZdzD61I7mYmj1NU1Oh6d1Vh13i4nMVMogRwGrlJLOczEqZ4/50dUKpdyR51w92Rl7+emxuYxCUh1lJ57vTUUvmIQphjAiSpV1g33kT7T4mjanixGnE/IqvxJl35TLBiaiyQlHB+02UvhqJ1E1UGo3OmcuApBRTU87emwuo8FUJL0W9/SIwgbzEY9M+WJt2on/jVjgafE1bU4XI04lKwcUDW1xYipDIi3ESY44MgXYYYxQldhtK+5LRQnAqxP37IvrsTmj2/vMOyi218Y6AhMvc+mRTHdj94aT6DdM7bcQqlZf0+Z0MeJUAjqq9sThMXinhTjFVniko1ovf5fYTaZRuc4oO2JOxDSQsnlpFC3nEC3TaclJaMuYWMjrCN0BqtXXtDn9KnHKTdS2gqtZcgSzSuvkXpaYA1lO9JfY7STuKxWnXPqngZjNmYLXdiRLfilAqfSP+4X2eOWZl+aqIlDvaxacfo04Mde9Qm8E5DJ2mJpYiVOIHV4nUm+wS/FK7CadrlScLOb/iJTNa8ovbVMvOA9X2hnXeBeppo5ciDlfs+D0a8SJKYemg50RT0tGiRMwOYjM9a0ctFac5uZCRohTyuayI5WuPlqKE1e5WrYJyJTPcnAC8r5mwelXiBONrznXlNtzMlKcgNeNiFY7xGvFKecb1iunLCNlc9mR5viaW0XTADtr67yhrKP13GPK1yw4/QpxOmFSfK1Rhfl1KjoYLU7AMy2w6uz/W1qXs/knpXX0pZ5VS7k8P2KDbszXPK1rwB7vE9Y94LaBI9IfRDL0PYvfrPemcBn/L8WpZbXOwg9KbN7SkSy+CbxCZ2MlfW6EOKV8TZvTRYsTPw3QdCrZsWou6/ayXj37cXIoaYec/ygVJ+0dz6U25wpUaUfS3pnP+Rut9rOeI85TS/maNqeLFScLYcLjfbGDscJDskg+f7NcSQGeo5nVvqESu60L75MRlubyfI3N5S71kghLc8uDtjABz8hpxKdNKV/T5nSR4hTbexRiAztD/uWck9VenFK7se25CO4k7tGaB6y1uYzeUtGG3LujmS6VCFONHTkoWO8ZI1K+ps3px4rTClPlD6iLfnhcx9xq0QXve18O0PkcZE6catvGA8ZSYkrnTK2SaLSt1G65nc7A60pd6JyjbT73xQBXlWIi2spp+DVBDDu8RiU88C33zhzfI32th9PYuz5SnMIjL0qIpZNekD4wXR56Rsh0RCPimROn2rbJzW8HvBqVne6SeI9W22qepwPG7mVKF3PekTYHXpfFw7LkF/ahn7dyKs85StUzFBr5HWIsMuQ8X6oTj/Q1oJ3TGIaKk5xrmNupHe5+nZtLoZOWTlBvg2fD//ekfHPiVNs2ubpB7g6YnJwfgKZGIY221diNkB2RdZs7bGykzcN3yKNX1njO4aSeqeU0dlJn6pLpWWwB5ojJJjzLKpcCjvQ1ooXTVF3MxWmHiaTY5HEq3NyIZ0hKDqn3x64T3gmmsTUmFn+RJ7a2bcA7h3TQ0qNdW9rWYjeJHzy5OD/+zjnmaJsTTH1O4t498jzVcLqtqOcZ7/M1a7zySP5LVuZG+xrRwmmI4WldC2IGs8IP7JbjY1hy23owkpceOKd2+HhxKjmoSxNzB5hpYslt68FoXnrgnNrho8Vpg/zkmzaOGHcM6pLb1oPRvPTAObVFlzjt8f7phtbeoRUmw486L3uHcSHvktvWg9G89MA51UXqM7BmcYpd1juhHQ7H8uB64nA4HA6Hw+FwOBwOh8PhcDgcDkcM/wAwZLX6P4KfpgAAAABJRU5ErkJggg==\" style=\"width: 147.5px; height: 18.5px;\" width=\"147.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 142px 8px; transform-origin: 142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e also doesn't qualify because although it has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAdklEQVRYhe2OwQmAMBAEp4d0kAbsw0bsIB3YQmqxB1uwF/0YCHiPyGEU3IHjXrMMCCG+RQTCC645loEdGDq6F0I1Vq511OOajEA6/3pz1OM2kRyjHldBClKQghSkIAX9MigCWzWaOrnm2AwsxmVgesgVQghRcwBVnXRb64UZ7QAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eproper divisors, some of its divisor, like \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have even number of proper divisors. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340px 8px; transform-origin: 340px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is considered a proper divisor of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = oddDivs(n)\r\n  s = n;\r\nend","test_suite":"%%\r\nn = 100;\r\ns_correct = 61;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 60794;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nns = 10000:50000;\r\nss = arrayfun(@(n) oddDivs(n),ns);\r\nss_correct = [729580926 12160 15197 18242 21278 24310 27360 30401 7020];\r\nassert(isequal([sum(ss) ss(10000:5000:40000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 123456789;\r\ns_correct = 75052724;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = intmax;\r\ns_correct = 1305513583;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = double(intmax)*10;\r\ns_correct = 13055135057;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nn = double(intmax)*200;\r\ns_correct = 261102702413;\r\nassert(isequal(oddDivs(n),s_correct))\r\n%%\r\nfiletext = fileread('oddDivs.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T04:54:26.000Z","updated_at":"2026-02-24T15:31:17.000Z","published_at":"2021-09-27T12:53:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is special. It has odd number of proper divisors:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,3,5,6,7,10,14,15,21,30,35,42,70,105]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Furthermore, if you take \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eany\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of its proper divisors, say \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e70\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it too has odd number of proper divisors: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,5,7,10,14,35]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have similar property as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find how many integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have similar property as 210, namely, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe integers should have odd number of proper divisors and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eall\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e its proper divisors have odd number of proper divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, as well. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, does not qualify because it has even proper divisors, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in total  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1,2,4,5,10,20,25,50]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e108\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e also doesn't qualify because although it has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eproper divisors, some of its divisor, like \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, have even number of proper divisors. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is considered a proper divisor of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52866,"title":"Easy Sequences 36: Hyperbolic Lattice Points","description":"The graph, shown below, of the hyperbola: , passes through four positive lattice points:.\r\n                                            \r\nIt can be shown that those  points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point  on the xy-plane where both  and  are integers.)\r\nGiven the integers  and , write a function that counts the number of positive lattice points that the hyperbola: , passes through.\r\nNOTE: The trivial point , is not to be included in the count.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 510px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 56px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe graph, shown below, of the hyperbola: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"35\" style=\"width: 61px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, passes through four positive lattice points:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be shown that those \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"19\" style=\"width: 39.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e on the xy-plane where both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are integers.)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 56px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven the integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a function that counts the number of positive lattice points that the hyperbola: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAABGCAYAAAAD4YAyAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAeqADAAQAAAABAAAARgAAAADCz8POAAAHR0lEQVR4Ae2afcxPZRjHPaloChVZwhZDVktZTW+MtN4widIb1SyqCf1Rk2pmapksUzbNmmmxspnV2lJGjJShrSyJZYZR8hIJkdTna+d6uh3H85zf8/Y7z+9c1/b5nfvc93XOuc73Pvd97vv+nQYN3FwBV8AVcAVcAVfAFXAFXAFXwBVwBVwBV8AVcAVcAVfAFXAFXAFXwBWoBwo0rAcxZjnE8wluIDwEfeEQNILhMBhWwzEw60xCvuIv2AZml5J4DvrBOgiPY9etWAoM4sK/wElYAQvhD/gB/oX9YA1JFbwRToDKhCpalStT+U6wsgnKdCu+Ai8Qgip4L1wbhDOetFXWgiC/CelOcA5MA/MZQroFbAE9LJ/BblDv4FZkBWZyfVWUuukbY7EMi8pUPjJWZrtdA5/ppNUTLIPzwC0jCjxKHNYahybENDko75BQrqwy+B3sPEpfAW4ZUaA5cfwKqiC9b9UNx20RGSrfGi+I7ZuffEfFyny3yAq8y/VVMeLhhFiakncgKp+dUB5mvRr56VzhOz70qdF00lNZoxcokZNpdKwpk2wHzD+VOv1nDLvNoqzlpxedsacRt9nNlvBt8RV4ghCsNX+UEI4qWO9a82mb4GNZendrIGe+c62gNrfeotOpe03gtiZIW3IcCb3DZVoEUatPsnPJVMV+B+sjhx7R1jcZUGAeMVgLvCsWz4PsJ7XQp8nvGfOdyL7m3m1gGtg525GW3QsjTqX8pygKvMxVrVKeDyJQxRyFcHClUfSzsAtuA/k0hgGglbH+INPSqZ1Tx3SBfdAb6tRacrU+MBr09F0GcXuEjDfgynhBie13436sUo6T/gS0inUSxoIq1Mq3k9ZS6A2gLlz5h0G+U8BMXf0RsPIDpKdaYV1tNarUyNCC1/b12MUvZ1/Bq2xNrKzUdsu4oUmgSjZNtpK+H2TtwfLVkm9SJrYBLF/df3xMNCsol+YNoc5NS3LDwALVkxoG2oj9zVG53jtprDtO6p6qy+I0F6sFn46c8z64DqRPaOp6bweta5tpWqauurNlxLZ6gHpCJqZYCwjEKjs+QryEMj21qyCN3YqTnas629VpLuY+/yug4X5lNgOHQZGTns6VwQH7Se+B5UFeRUk9FCMrckhZpt7FrYYVUHf9G6gF/hg7d2v2j0OHWL7v1lMFNMm3rrZVcA+vkf482PdkPVdgKPFbRQ+O7kXTLS0UaGrhlnEF0ryjdQtfBvehkbMGaFokWAdfQVrTsZp/Vte+5QR3VvckfnyyAj+TrVa9BK4GvZu1KFCI1fWoeyzBWU+Ux20vq5y0LVr+K0CDruvhbfgQ1KILMR91F6JWkXy1SG+tQqtm/vlLkSqiti+rbtoqWpXuVqIKtOG+VNFLQUt3biWqwFPc159Q6v9UlWj1pbstDcL0N9pj6dzdq5YU0IeED8A4eB/Wwtn+MKGoMLsQ9/XwZmGHuXctKPAB59wINlY6SrpRVa/TmwPfA30ZcRHonaxFDq15uxVfgaaEYBUdLmQVHJnmunaiE6S1Clblp6bgq/sBlSmg/66tfsZX5lxR+eToRPp8dRJ4S65Irbov09KzVXShK5NnRKuR9QVn5HpGFhTQCqUqei94I8xCjdRCDBoz/Q2qaC1Bp7ZC1rpTnzTjjpqO3AHtQV9zqoWY6Ruv4XAx6BV2ELJkvQjG6mxxFJg+0tRHipoC63Wrjww3Q25NFaypiQaY9o7Tmr0qV6bynWBlE5SZMXuHeCw+/dcwBg4HeSrTolau1zuaIEAn0HtN36mbYENIt4AtoNatqeRu6AtZs58ISHFrZvQi/AMz4XH4GOye9pHWfebeuqKAiTKd9EJYBvFPeMnKjLUjEov5e9LHIP4wfh34dCedeytDAb3PTDils/63q8YOFq+2z0Dc5pBhPuqpys1e7OUZOUlIjNVwd3S/mpvq/VyIad1ZK1N6aKpqWlrWSmQaCz+dWsUB6rLj1izI2B6kc50MFx5UaYWaKshaT1W3+vYtjel9q3mzXadXwkHy2RH5HGWrqVi55bVFSwCNuM20rKjWVYhtwnlkIQck+Kry0lg3nGx2oPfz8oSD+pDXJsr/lO2hBJ/cZWnOKSGshczNuAIvBbE+eZZYv4h8jrC96iw+ucpWL/YNrAS1DlX2NsiyLSM4xak5c+OEQPtF5fIZnVCey6yJ3LW6THVz00DiCE1fZPp7dsSpVDZ+NP8/BopxaUJIrcnbFZUvYVuW4JOLrPbcpSpPLWEAnID+IBsIVtGjSHcBLTb0hqyYYrcY34oF1ZL9tVG5um4t/OTWbCSqbu8kTAmUaE5a7zQJqXJ9LjUVsmRaAbOKnhEFphH2PaCWrAf3FVBerm0Dd29CzSMdF2RWUD6fdEPIkrUimDmgf61UqZodHAQtfy6CHlCp5aE/17TkFtA/OpsSFJEGEktCapCWVWtKYB2hLewB3YvGGm6ugCvgCrgCroAr4Aq4Aq6AK+AKuAKugCtQwwr8B5KzJmJZm/iGAAAAAElFTkSuQmCC\" width=\"61\" height=\"35\" style=\"width: 61px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, passes through.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe trivial point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"19\" style=\"width: 36px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is not to be included in the count.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numPosLat(a,b)\r\n  y = x;\r\nend","test_suite":"%%\r\na = 2; b = 4;\r\nn_correct = 4;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 12; b = 28;\r\nn_correct = 20;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 100; b = 1000;\r\nn_correct = 36;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 123; b = 456;\r\nn_correct = 48;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = 12345; b = 54321;\r\nn_correct = 48;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\nas = floor(linspace(201,1234,100)); bs = floor(linspace(401,5678,100));\r\nns = arrayfun(@(i) numPosLat(as(i),bs(i)),1:100);\r\nss = floor([sum(ns) mean(ns) mode(ns) median(ns) std(ns)]);\r\nss_correct = [4750 47 48 32 43];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\na = 35153041; b = 12117386241;\r\nn_correct = 975;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = floor(double(intmax)/7); b = floor(double(intmax)/3);\r\nn_correct = 1944;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\na = floor(double(intmax)/5); b = double(intmax);\r\nn_correct = 8;\r\nassert(isequal(numPosLat(a,b),n_correct))\r\n%%\r\nfiletext = fileread('numPosLat.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-06T10:44:57.000Z","updated_at":"2026-02-24T17:29:27.000Z","published_at":"2021-10-06T19:09:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe graph, shown below, of the hyperbola: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\frac{2x}{x-4}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, passes through four positive lattice points:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{(5,10),\\\\ (6,6),\\\\ (8,4),\\\\ (12,3)\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"293\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"309\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be shown that those \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(n,m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on the xy-plane where both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that counts the number of positive lattice points that the hyperbola: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\frac{ax}{x-b}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, passes through.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe trivial point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is not to be included in the 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Sequences 98: One-line Code Challenge - Ternary Operator Function","description":"Ternary operation is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\r\n    y = (p \u003e q) ? m : n;\r\nwhich means that y is assigned the value of either m or n, depending on whether the statement (p \u003e q) is true or false, respectively.\r\nUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\r\n    if p \u003e q\r\n        y = m;\r\n    else\r\n        y = n;\r\n    end\r\nBut that is 5 lines of Matlab code versus just a single line in C!\r\nIn this problem we are required create the function ternaryFunc, which takes on the following parameters:  data values a and b; a conditional function C, that outputs true or false, and functions T and F which are applied to a and b, depending on the value of C(a,b). We can write the function as follows:\r\n    function x = ternaryFunc(a,b,C,T,F)\r\n        if C(a,b)\r\n            x = T(a,b);\r\n        else\r\n            x = F(a,b);\r\n        end\r\n    end\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nUse of if, while and switch statements is not allowed.\r\nRegular expressions and string manipulation are not allowed.\r\nUse of variable length arguments is not allowed.\r\n-------------\r\nHINT:  As an exercise you may want to first solve Problem #44243.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390px; transform-origin: 407px 390px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Ternary_conditional_operator\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eTernary operation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    y = (p \u0026gt; q) ? m : n;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich means that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is assigned the value of either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003em \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, depending on whether the statement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e(p \u0026gt; q) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis true or false, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 100px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 50px; transform-origin: 404px 50px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eif \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ep \u0026gt; q\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        y = m;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eelse\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        y = n;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBut that is 5 lines of Matlab code versus just a single line in C!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this problem we are required \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecreate the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eternaryFunc\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, which takes on the following parameters:  data values \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e; a conditional function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that outputs true or false, and functions T and F which are applied to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, depending on the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eC(a,b)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We can write the function as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 140px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 70px; transform-origin: 404px 70px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = ternaryFunc(a,b,C,T,F)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eif \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eC(a,b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e            x = T(a,b);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eelse\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e            x = F(a,b);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 100px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 50px; transform-origin: 391px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eif\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ewhile\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eswitch\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e statements is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions and string manipulation are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse of variable length arguments is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHINT:  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAs an exercise you may want to first solve \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44243\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003eProblem #44243\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = ternaryFunc(a,b,C,T,F)\r\n    if C(a,b)\r\n        x = T(a,b);\r\n    else\r\n        x = F(a,b);\r\n    end\r\nend","test_suite":"%%\r\na = 20; b = 2; \r\nC = @gt;\r\nT = @(a,b) a ^ b;\r\nF = @(a,b) b ^ a;\r\nx_correct = 400;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\nC = @le;\r\nx_correct = 1048576;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 123; b = 456; \r\nC = @lt;\r\nT = @(a,b) round(sind(b/a),4);\r\nF = @(a,b) round(sind(b*a),4);\r\nx_correct = 0.0647;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\nC = @ge;\r\nx_correct = -0.9511;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 'A'; b = 'A'; \r\nC = @eq;\r\nT = @(a,b) log(a/b);\r\nF = @(a,b) log(a*b);\r\nx_correct = false;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 1000; b = 2000; \r\nC = @gt;\r\nT = @(a,b) char(a + \" is greater than \" + b);\r\nF = @(a,b) char(b + \" is greater than \" + a);\r\nx_correct = '2000 is greater than 1000';\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = repelem('1',5); b = repelem('2',100); \r\nC = @(a,b) all(lt(a,b(1:length(a))));\r\nT = @(a,b) arrayfun(@(i) i,1:str2num(a));\r\nF = @(a,b) arrayfun(@(i) i,1:str2num(b));\r\nx_correct = 1:11111;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = 1; b = 0; \r\nC = @lt;\r\nT = @(a,b) a * length(1:1/b);\r\nF = @(a,b) b * length(1:1/a);\r\nx_correct = 0;\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\na = randi(1000); b = randi(1000); \r\nC = @le;\r\nT = @(a,b) a * length(1:b/a);\r\nF = @(a,b) b * length(1:a/b);\r\nif C(a,b)\r\n    x_correct = T(a,b);\r\nelse\r\n    x_correct = F(a,b);\r\nend\r\nassert(isequal(ternaryFunc(a,b,C,T,F),x_correct))\r\n%%\r\nfiletext = fileread('ternaryFunc.m');\r\nnot_allowed = contains(filetext, 'str2') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'if') || contains(filetext, 'while') || contains(filetext, 'switch') || contains(filetext, 'vararg');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n    if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n        c = c + numel(find(s{1}==';'));\r\n        if  ~isequal(s{1}(end),';')\r\n            c = c + 1;\r\n        end\r\n    end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":255988,"edited_by":255988,"edited_at":"2023-03-29T18:12:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2023-03-01T19:53:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-26T08:27:07.000Z","updated_at":"2026-02-27T16:09:27.000Z","published_at":"2023-02-27T08:38:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Ternary_conditional_operator\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTernary operation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a standard construct in most computer languages. The ternary operator assigns value to a variable depending on the result of the condition. For example, we find the following syntax in C and many C-like languages:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    y = (p \u003e q) ? m : n;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich means that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is assigned the value of either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, depending on whether the statement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p \u0026gt; q) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis true or false, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, Matlab does not have a ternary operator and if we need to get the same effect, we may write the statement this way:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    if p \u003e q\\n        y = m;\\n    else\\n        y = n;\\n    end]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut that is 5 lines of Matlab code versus just a single line in C!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem we are required \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecreate the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eternaryFunc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which takes on the following parameters:  data values \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e; a conditional function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that outputs true or false, and functions T and F which are applied to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, depending on the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC(a,b)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. We can write the function as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    function x = ternaryFunc(a,b,C,T,F)\\n        if C(a,b)\\n            x = T(a,b);\\n        else\\n            x = F(a,b);\\n        end\\n    end]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eif\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswitch\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e statements is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions and string manipulation are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse of variable length arguments is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHINT:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eAs an exercise you may want to first solve \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44243\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem #44243\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52978,"title":"Easy Sequences 44: Finding the Smallest Number whose Cube is divisible by a Factorial","description":"Given a integer , our goal is to find the smallest integer , such that  divides .\r\nFor example, for , , because , (since ), and  is the smallest number that has this property. Please present the value of  in modulo  (a prime number).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 83px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven a integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, our goal is to find the smallest integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18\" style=\"width: 15.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e divides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 53px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"18\" style=\"width: 43.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, because \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"54.5\" height=\"20\" style=\"width: 54.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, (since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"32\" style=\"width: 59px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the smallest number that has this property. Please present the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e in modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (a prime number).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = SCDF(n)\r\n    k = mod(10*n,1000000123);\r\nend","test_suite":"%%\r\nn = 6;\r\nk_correct = 60;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 10;\r\nk_correct = 2520;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 100;\r\nk_correct = 29482652;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 1234;\r\nk_correct = 27609071;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 123456;\r\nk_correct = 34685960;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = 22222222;\r\nk_correct = 27608842;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nn = floor(double(intmax)/100);\r\nk_correct = 12770769;\r\nassert(isequal(SCDF(n),k_correct))\r\n%%\r\nns = floor(double(intmax)./(20001:20050));\r\nks = arrayfun(@(n) SCDF(n),ns);\r\nss = floor([mean(ks) mode(ks) median(ks) std(ks)]);\r\nss_correct = [27662018 2442880 25739266 15619436];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('SCDF.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-28T11:43:38.000Z","updated_at":"2026-03-24T12:58:42.000Z","published_at":"2021-10-29T14:06:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, our goal is to find the smallest integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e divides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek=60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, because \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6!\\\\ | \\\\ 60^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, (since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac_{60^3}_{6!} = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smallest number that has this property. Please present the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e59999999\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (a prime number).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56458,"title":"Easy Sequences 80: Sum of the n-th Row of Fibonacci Square Triangle","description":"We shall call the following arrangement of Fibonacci numbers, as the Fibonacci Square Triangle:\r\n                        \r\nwhere:  and  for .\r\nWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. ), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\r\nIn this problem, we are required to find the sum of the n-th row of the Fibonacci Square Triangle. For example for the 4th row, the sum is:\r\n        \r\nSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\r\nTherefore, for the 4th row, your program output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 445px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 222.5px; transform-origin: 407px 222.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe shall call the following arrangement of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, as the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFibonacci Square Triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 150px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75px; text-align: left; transform-origin: 384px 75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"167\" height=\"19\" style=\"width: 167px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"20\" style=\"width: 38px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this problem, we are required to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efind the sum of the n-th row of the Fibonacci Square Triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. For example for the 4th row, the sum is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"429.5\" height=\"21\" style=\"width: 429.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for the 4th row, your program output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"102.5\" height=\"19\" style=\"width: 102.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumFST(n)\r\n    s = [4791 4791 4];\r\nend","test_suite":"%%\r\nn = 4:8;\r\ns_correct = {[4791 4791 4] [5971 7175 6] [1932 2536 9] [1632 8113 12] [3605 8865 15]};\r\nassert(isequal(arrayfun(@(i) sumFST(i),n,'uni',0),s_correct))\r\n%%\r\nn = 10;\r\ns_correct = [3152 5555 23];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 50;\r\ns_correct = [2682 1525 533];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = [1928 7575 2111];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 500;\r\ns_correct = [8201 1625 52351];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 600:100:1000;\r\ns_correct = 742673;\r\nassert(isequal(sum(arrayfun(@(i) sum(sumFST(i)),n)),s_correct))\r\n%%\r\nn = 100:10:1000;\r\ns_correct = 7865124;\r\nassert(isequal(sum(arrayfun(@(i) sum(sumFST(i)),n)),s_correct))\r\n%%\r\nn = 1234;\r\ns_correct = [3836 6419 318495];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 123456;\r\ns_correct = [1647 8064 3185286664];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = [1345 9375 208987849238];\r\nassert(isequal(sumFST(n),s_correct))\r\n%%\r\nfiletext = fileread('sumFST.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":255988,"edited_by":255988,"edited_at":"2022-11-17T19:00:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-04T19:35:14.000Z","updated_at":"2026-03-23T18:26:25.000Z","published_at":"2022-11-08T12:04:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe shall call the following arrangement of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, as the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci Square Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)^2\\\\\\\\F(2)^2,\\\\ F(3)^2\\\\\\\\F(4)^2,\\\\ F(5)^2,\\\\ F(6)^2\\\\\\\\F(7)^2,\\\\ F(8)^2,\\\\ F(9)^\\\\ F(10)^2\\\\\\\\F(11)^2,\\\\ F(12)^2,\\\\ F(13)^2,\\\\ F(14)^2,\\\\ F(15)^2\\\\\\\\F(16)^2,\\\\ F(17)^2,\\\\ F(18)^2,\\\\ F(19)^2,\\\\ F(20)^2,\\\\ F(21)^2\\\\\\\\....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)=F(2)=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(i)=F(i-1)+F(i-2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u0026gt;2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe can see from the above list, that the first row contains the square of the first Fibonacci number (i.e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF(1)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), the 2nd row contains the squares of the next 2 Fibonacci numbers, the 3rd  contains the next 3, the 4th contains the next 4, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, we are required to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efind the sum of the n-th row of the Fibonacci Square Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example for the 4th row, the sum is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_4 = F(7)^2+F(8)^2+F(9)^2+F(10)^2=13^2+21^2+34^2+55^2=4791\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince, Fibonacci number squares grows very fast, please present your answer as a row vector of 3 elements. The first element is the first 4 digits of the sum, the second element is the last 4 digits of the sum, and last element is the number of digits of the sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for the 4th row, your program output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4791,\\\\  4791,\\\\ 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