{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-08-24T00:15:41.000Z","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":"2026-08-24T00:00:00.000Z","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":43010,"title":"kmph to mph converter","description":"Convert the speed in miles/hour to km/hour.","description_html":"\u003cp\u003eConvert the speed in miles/hour to km/hour.\u003c/p\u003e","function_template":"function y = mph2kmph(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1.60934;\r\nassert(isequal(mph2kmph(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 16.0934;\r\nassert(isequal(mph2kmph(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 8.0467;\r\nassert(isequal(mph2kmph(x),y_correct))\r\n\r\n%%\r\nx = 50;\r\ny_correct = 80.467;\r\nassert(isequal(mph2kmph(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":195,"test_suite_updated_at":"2016-10-04T04:45:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T04:43:44.000Z","updated_at":"2026-05-20T14:47:43.000Z","published_at":"2016-10-04T04:43:44.000Z","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\u003eConvert the speed in miles/hour to km/hour.\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":45563,"title":"Times 10","description":"Try out this test problem first.\r\n\r\nGiven the variable x as your input, multiply it by ten and put the result in y.\r\n\r\nExamples:\r\n\r\n Input  x = 1\r\n Output y is 10\r\n Input  x = 2\r\n Output y is 20\r\n\r\n","description_html":"\u003cp\u003eTry out this test problem first.\u003c/p\u003e\u003cp\u003eGiven the variable x as your input, multiply it by ten and put the result in y.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input  x = 1\r\n Output y is 10\r\n Input  x = 2\r\n Output y is 20\u003c/pre\u003e","function_template":"function y = times10(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(times10(1),10));,,\r\n\r\n%%\r\nassert(isequal(times10(2),20));,\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":445209,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":126,"test_suite_updated_at":"2020-05-21T15:25:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-21T15:23:45.000Z","updated_at":"2026-05-30T14:17:52.000Z","published_at":"2020-05-21T15:25:12.000Z","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\u003eTry out this test problem first.\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\u003eGiven the variable x as your input, multiply it by ten and put the result in 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\u003eExamples:\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[ Input  x = 1\\n Output y is 10\\n Input  x = 2\\n Output y is 20]]\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":43479,"title":"Modulation index","description":"The amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.","description_html":"\u003cp\u003eThe amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.\u003c/p\u003e","function_template":"function z = your_fcn_name(x,y)\r\n  z = ;\r\nend","test_suite":"%%\r\nx = 8; y=2;\r\nz_correct = 4;\r\nassert(isequal(your_fcn_name(x,y),z_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":87885,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-11T22:34:12.000Z","updated_at":"2026-02-06T15:38:09.000Z","published_at":"2016-10-11T22:34:12.000Z","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\u003eThe amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.\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":43033,"title":"Create a constant offset.","description":"Add a constant offset to an array.\r\n\r\nExample\r\n\r\n a = [1 3 5 9]\r\n offset = 2\r\n y = [3 5 7 11]","description_html":"\u003cp\u003eAdd a constant offset to an array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e a = [1 3 5 9]\r\n offset = 2\r\n y = [3 5 7 11]\u003c/pre\u003e","function_template":"function y = constant_offset(a,offset)\r\n  y = a;\r\nend","test_suite":"%%\r\na = 1;\r\noffset = 2\r\ny_correct = 3;\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n\r\n%%\r\na = [-1 1];\r\noffset = 2\r\ny_correct = [1 3];\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n\r\n%%\r\na = [-10:1:1];\r\noffset = 10\r\ny_correct = [0:11];\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":0,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":136,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T08:20:41.000Z","updated_at":"2026-04-22T17:38:49.000Z","published_at":"2016-10-05T08:20:41.000Z","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\u003eAdd a constant offset to an array.\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\u003eExample\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 = [1 3 5 9]\\n offset = 2\\n y = [3 5 7 11]]]\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":2378,"title":"Area of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n  A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1005,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-08-14T17:22:23.000Z","published_at":"2014-06-18T17:40:40.000Z","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\u003eA triangle is given with base\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\u003e'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\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\u003e'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\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":45430,"title":"Juego de posiciones","description":"Crea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor. \r\n\r\nPor ejemplo:\r\n\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\n\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\n\r\nPD: Considerad el cero como número positivo. ","description_html":"\u003cp\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/p\u003e\u003cp\u003ePor ejemplo:\u003c/p\u003e\u003cp\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/p\u003e\u003cp\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/p\u003e\u003cp\u003ePD: Considerad el cero como número positivo.\u003c/p\u003e","function_template":"function x = order(y)\r\n \r\nend","test_suite":"%%\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\ny=[6 7 -34 9 0];\r\ny_correct= [-34 9 7 6 0];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":394942,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-09T11:48:17.000Z","updated_at":"2026-08-18T12:08:53.000Z","published_at":"2020-04-10T07:53:03.000Z","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\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePor ejemplo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [-1 6 15 -7 31 2 -4 -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\u003ey_correct = [-7 -5 -4 -1 31 15 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\u003ePD: Considerad el cero como número positivo.\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":45568,"title":"Times 5","description":"Try out this test problem first.\r\n\r\nGiven the variable x as your input, multiply it by five and put the result in y.\r\n\r\nExamples:\r\n\r\nInput  x = 1\r\n Output y is 5\r\n Input  x = 2\r\n Output y is 10","description_html":"\u003cp\u003eTry out this test problem first.\u003c/p\u003e\u003cp\u003eGiven the variable x as your input, multiply it by five and put the result in y.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003eInput  x = 1\r\n Output y is 5\r\n Input  x = 2\r\n Output y is 10\u003c/p\u003e","function_template":"function y = times5(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(times5(1),5));\r\n\r\n%%\r\nassert(isequal(times5(2),10));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":443529,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":119,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-21T15:30:36.000Z","updated_at":"2026-05-30T14:17:53.000Z","published_at":"2020-05-21T15:30:36.000Z","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\u003eTry out this test problem first.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 the variable x as your input, multiply it by five and put the result in 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput x = 1 Output y is 5 Input x = 2 Output y is 10\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":42986,"title":"Determine the roots of a cubic equation","description":"Given the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.","description_html":"\u003cp\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/p\u003e","function_template":"function y = cubicRoots(a,b,c,d)\r\n  y = [0 0 0];\r\nend","test_suite":"%%\r\na=1; b=3; c=3; d=1;\r\ny_correct = [-1 -1 -1];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=1; b=-6; c=11; d=-6;\r\ny_correct = [1 2 3];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=4; b=4; c=-1; d=-1;\r\ny_correct = [-1 -0.5 0.5];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":"2016-09-30T16:42:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:40:42.000Z","updated_at":"2026-05-28T15:58:44.000Z","published_at":"2016-09-16T10:40:42.000Z","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\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\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":1355,"title":"Given area find sides","description":"In a right angle triangle given area 'A' \r\none arm=x, another arm=2x\r\nthen find the value of x.\r\n\r\nFor example, area A=400 then x=20;","description_html":"\u003cp\u003eIn a right angle triangle given area 'A' \r\none arm=x, another arm=2x\r\nthen find the value of x.\u003c/p\u003e\u003cp\u003eFor example, area A=400 then x=20;\u003c/p\u003e","function_template":"function y = findside(A)\r\n  y = x+2x;\r\nend","test_suite":"%%\r\nA = 400;\r\ny_correct = 20;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 144;\r\ny_correct = 12;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 225;\r\ny_correct = 15;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 256;\r\ny_correct = 16;\r\nassert(isequal(findside(A),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":6975,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":567,"test_suite_updated_at":"2013-03-18T04:52:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-18T04:15:57.000Z","updated_at":"2026-07-28T18:16:54.000Z","published_at":"2013-03-18T04:23:49.000Z","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\u003eIn a right angle triangle given area 'A' one arm=x, another arm=2x then find the value of 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, area A=400 then x=20;\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":60321,"title":"Area of right triangle","description":"Given a hypotenuse and a leg , calculate the area of right triangle.","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 10.5px; transform-origin: 407.5px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a hypotenuse and a leg , calculate the area of right triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area(b,c)\r\n  y = b+c;\r\nend","test_suite":"%%\r\nb=4\r\nc=5\r\ny_correct = 6;\r\nassert(isequal(area(b,c),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4201661,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-15T21:08:41.000Z","updated_at":"2026-06-05T04:53:12.000Z","published_at":"2024-05-15T21:08:41.000Z","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:t\u003eGiven a hypotenuse and a leg , calculate the area of right triangle.\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":57725,"title":"Sequence problem","description":"find the nth term of the sequence:\r\n790\r\n1303\r\n2033\r\n____\r\n4366\r\n6095\r\n","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: 194.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.3125px; transform-origin: 407px 97.3125px; 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=\"\"\u003efind the nth term of the sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3125px; transform-origin: 391px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e790\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1303\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e2033\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"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\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4366\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6095\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sequence(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfunctions={'polyfit','polyval'};\r\nassessFunctionAbsence(functions, 'FileName', 'sequence.m');\r\n\r\n%%\r\nx = 1;\r\ny_correct = 790;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1303;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 6095;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 8293;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 18511;\r\nassert(isequal(sequence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2900827,"edited_by":2900827,"edited_at":"2023-02-20T05:07:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2023-02-20T05:07:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-19T16:34:33.000Z","updated_at":"2026-06-03T23:09:03.000Z","published_at":"2023-02-19T16:35:26.000Z","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\u003efind the nth term of the sequence:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e790\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1303\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2033\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=\\\"2\\\"/\u003e\u003c/w:numPr\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=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4366\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6095\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\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":58847,"title":"Possible American Football Scoring Combinations","description":"With inspiration from Problem 56195. Possible Ruby Scores, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (Official NFL Scoring Plays). \r\nIn American football, the 7 possible ways of scoring are:\r\nTouchdown - 6 points\r\nTry after touchdown - 1 point\r\nTry after touchdown - 2 points\r\nSafety - 2 points\r\nField Goal - 3 points\r\nDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\r\nDefensive \"touchdown\" on try after touchdown - 2 points\r\nValues for score1 and score2 include all natural numbers (realistically \u003c100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\r\n*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by the opposing team.\r\nExample\r\n[t1_combs, t2_combs] = amerfootballscores(5, 8)\r\n\r\nt1_combs =\r\n\r\n     0     0     0     0     1     0     1\r\n     0     0     0     1     1     0     0\r\n     0     0     0     2     0     1     0\r\n\r\n\r\nt2_combs =\r\n\r\n     0     0     0     1     2     0     0\r\n     0     0     0     4     0     0     0\r\n     1     0     0     1     0     0     0\r\n     1     0     1     0     0     0     0\r\nThis system is known as a linear Diophantine equation, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\r\nEach team's score can be modeled by the following equation:\r\n6(tds) + 1(off. 1 pt. pats) + 2(off. 2 pt. pats) + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\r\n    \u003e\u003e\u003e with the added constraints:\r\n                off. 1 pt. pats + off. 2 pt. pats \u003c= tds\r\n                def. 1pt. pats + def. 2pt. pats \u003c= tds for opponent","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: 970.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 485.312px; transform-origin: 407px 485.312px; 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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWith inspiration from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56195-possible-rugby-scores\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56195. Possible Ruby Scores\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, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://operations.nfl.com/the-rules/nfl-video-rulebook/scoring-plays/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOfficial NFL Scoring Plays\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: 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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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 American football, the 7 possible ways of scoring are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTouchdown - 6 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTry after touchdown - 1 point\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTry after touchdown - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSafety - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eField Goal - 3 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDefensive \"touchdown\" on try after touchdown - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eValues for score1 and score2 include all natural numbers (realistically \u0026lt;100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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-style: italic; \"\u003e*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by 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-style: italic; text-decoration: underline; text-decoration-line: underline; \"\u003eopposing team\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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-style: italic; \"\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 306.562px; 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 153.275px; transform-origin: 404px 153.281px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[t1_combs, t2_combs] = amerfootballscores(5, 8)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003et1_combs =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     0     1     0     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     1     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     2     0     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003et2_combs =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     1     2     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     4     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1     0     0     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1     0     1     0     0     0     0\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-collapse: preserve; 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=\"\"\u003eThis system is known as a 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 equation\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, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach team's score can be modeled by the following equation:\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6(tds) + 1(off. 1 pt. pats) + 2\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 0.8px; border-bottom-style: solid; border-bottom-width: 0.8px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003eoff. 2 pt. pats\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 0.8px; border-bottom-style: solid; border-bottom-width: 0.8px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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    \u0026gt;\u0026gt;\u0026gt; with the added constraints:\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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                off. 1 pt. pats + off. 2 pt. pats \u0026lt;= tds\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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                def. 1pt. pats + def. 2pt. pats \u0026lt;= tds for opponent\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t1_combs,t2_combs] = amerfootballscores(s1,s2)  \r\nt1_combs = [];  \r\nt2_combs = [];\r\n\r\nend","test_suite":"%%\r\ns1 = 5;\r\ns2 = 8;\r\nteam1 = [0     0     0     0     1     0     1;\r\n         0     0     0     1     1     0     0;\r\n         0     0     0     2     0     1     0];\r\nteam2 = [0     0     0     1     2     0     0;\r\n         0     0     0     4     0     0     0;\r\n         1     0     0     1     0     0     0;\r\n         1     0     1     0     0     0     0];\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\nassert(isequal([t1_combs;t2_combs],[team1;team2]))\r\n\r\n%%\r\ns1 = 0;\r\ns2 = 28;\r\nteam1 = [0     0     0     0     0     0     0];\r\nteam2 = [0     0     0     2     8     0     0;\r\n         0     0     0     5     6     0     0;\r\n         0     0     0     8     4     0     0;\r\n         0     0     0    11     2     0     0;\r\n         0     0     0    14     0     0     0;\r\n         1     0     0     2     6     0     0;\r\n         1     0     0     5     4     0     0;\r\n         1     0     0     8     2     0     0;\r\n         1     0     0    11     0     0     0;\r\n         1     0     1     1     6     0     0;\r\n         1     0     1     4     4     0     0;\r\n         1     0     1     7     2     0     0;\r\n         1     0     1    10     0     0     0;\r\n         1     1     0     0     7     0     0;\r\n         1     1     0     3     5     0     0;\r\n         1     1     0     6     3     0     0;\r\n         1     1     0     9     1     0     0;\r\n         2     0     0     2     4     0     0;\r\n         2     0     0     5     2     0     0;\r\n         2     0     0     8     0     0     0;\r\n         2     0     1     1     4     0     0;\r\n         2     0     1     4     2     0     0;\r\n         2     0     1     7     0     0     0;\r\n         2     0     2     0     4     0     0;\r\n         2     0     2     3     2     0     0;\r\n         2     0     2     6     0     0     0;\r\n         2     1     0     0     5     0     0;\r\n         2     1     0     3     3     0     0;\r\n         2     1     0     6     1     0     0;\r\n         2     1     1     2     3     0     0;\r\n         2     1     1     5     1     0     0;\r\n         2     2     0     1     4     0     0;\r\n         2     2     0     4     2     0     0;\r\n         2     2     0     7     0     0     0;\r\n         3     0     0     2     2     0     0;\r\n         3     0     0     5     0     0     0;\r\n         3     0     1     1     2     0     0;\r\n         3     0     1     4     0     0     0;\r\n         3     0     2     0     2     0     0;\r\n         3     0     2     3     0     0     0;\r\n         3     0     3     2     0     0     0;\r\n         3     1     0     0     3     0     0;\r\n         3     1     0     3     1     0     0;\r\n         3     1     1     2     1     0     0;\r\n         3     1     2     1     1     0     0;\r\n         3     2     0     1     2     0     0;\r\n         3     2     0     4     0     0     0;\r\n         3     2     1     0     2     0     0;\r\n         3     2     1     3     0     0     0;\r\n         3     3     0     2     1     0     0;\r\n         4     0     0     2     0     0     0;\r\n         4     0     1     1     0     0     0;\r\n         4     0     2     0     0     0     0;\r\n         4     1     0     0     1     0     0;\r\n         4     2     0     1     0     0     0;\r\n         4     2     1     0     0     0     0;\r\n         4     4     0     0     0     0     0];\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\nassert(isequal([t1_combs;t2_combs],[team1;team2]))\r\n\r\n%%\r\ns1 = 37;\r\ns2 = 49;\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\n% Matrices are rather large, so test case is dependent on the size of each output matrix, \r\n% where the number of rows will equate to the total number of scoring combinations\r\n[t1_rows,t1_cols] = size(t1_combs);\r\n[t2_rows,t2_cols] = size(t2_combs);\r\nassert(isequal([t1_rows,t2_rows],[2894,5625]))\r\n\r\n%%\r\ns1 = 37;\r\ns2 = 49;\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\n% Matrices are rather large, so test case is dependent on the sums of each column. These\r\n% values don't have any practical application.\r\nt1_sums = [6724, 2210, 1774, 10752, 6776, 7566, 5789];\r\nt2_sums = [19476, 6398, 5272, 28518, 18222, 11185, 9470];\r\nassert(isequal([t1_sums;t2_sums],[sum(t1_combs);sum(t2_combs)]))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":3499438,"edited_by":3499438,"edited_at":"2023-08-17T23:02:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-09T17:04:20.000Z","updated_at":"2026-06-04T20:28:24.000Z","published_at":"2023-08-10T05:17:56.000Z","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\u003eWith inspiration from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56195-possible-rugby-scores\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56195. Possible Ruby Scores\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://operations.nfl.com/the-rules/nfl-video-rulebook/scoring-plays/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOfficial NFL Scoring Plays\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:t\u003eIn American football, the 7 possible ways of scoring are:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTouchdown - 6 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry after touchdown - 1 point\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry after touchdown - 2 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSafety - 2 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eField Goal - 3 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefensive \\\"touchdown\\\" on try after touchdown - 2 points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValues for score1 and score2 include all natural numbers (realistically \u0026lt;100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eopposing team\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\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[[t1_combs, t2_combs] = amerfootballscores(5, 8)\\n\\nt1_combs =\\n\\n     0     0     0     0     1     0     1\\n     0     0     0     1     1     0     0\\n     0     0     0     2     0     1     0\\n\\n\\nt2_combs =\\n\\n     0     0     0     1     2     0     0\\n     0     0     0     4     0     0     0\\n     1     0     0     1     0     0     0\\n     1     0     1     0     0     0     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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis system is known as a 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 equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach team's score can be modeled by the following equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6(tds) + 1(off. 1 pt. pats) + 2(off. 2 pt. pats) + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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    \u0026gt;\u0026gt;\u0026gt; with the added constraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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                off. 1 pt. pats + off. 2 pt. pats \u0026lt;= tds\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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                def. 1pt. pats + def. 2pt. pats \u0026lt;= tds for opponent\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":47,"title":"Extract leading non-zero digit","description":"\u003chttp://en.wikipedia.org/wiki/Benford%27s_law Benford's Law\u003e states that the distribution of leading digits is not random.  This is probably because many things grow logarithmically.  Extract the leading digit from these vectors.\r\n\r\n* 10 --\u003e 1 \r\n* 13 --\u003e 1 \r\n* 0.3 --\u003e 3\r\n* -4 --\u003e 4 \r\n* -5 --\u003e 5 \r\n* -0.006 --\u003e 6\r\n\r\nInput will be a vector\r\n\r\n x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];\r\n\r\nOutput should be\r\n\r\n y = [1 3 2 1 6 5 3];\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Benford%27s_law\"\u003eBenford's Law\u003c/a\u003e states that the distribution of leading digits is not random.  This is probably because many things grow logarithmically.  Extract the leading digit from these vectors.\u003c/p\u003e\u003cul\u003e\u003cli\u003e10 --\u003e 1\u003c/li\u003e\u003cli\u003e13 --\u003e 1\u003c/li\u003e\u003cli\u003e0.3 --\u003e 3\u003c/li\u003e\u003cli\u003e-4 --\u003e 4\u003c/li\u003e\u003cli\u003e-5 --\u003e 5\u003c/li\u003e\u003cli\u003e-0.006 --\u003e 6\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eInput will be a vector\u003c/p\u003e\u003cpre\u003e x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];\u003c/pre\u003e\u003cp\u003eOutput should be\u003c/p\u003e\u003cpre\u003e y = [1 3 2 1 6 5 3];\u003c/pre\u003e","function_template":"function y = leadingDigit(x)\r\n  y = x\r\nend","test_suite":"%%\r\nx = [100 23 -34 0.005 -0.466664 -0.555 1 134534];\r\ny_correct = [1 2 3 5 4 5 1 1];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [57 -0.2 8913 -63 0.838127];\r\ny_correct = [5 2 8 6 8];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [-0.4336    0.3426    3.5784    2.7694   -1.3499];\r\ny_correct = [4 3 3 2 1];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [0.3000 -0.1 -0.00000002 0.5 0.002];\r\ny_correct = [3 1 2 5 2];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":5,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2256,"test_suite_updated_at":"2012-05-29T14:34:23.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:23.000Z","updated_at":"2026-08-15T02:28:08.000Z","published_at":"2012-01-18T01:00:23.000Z","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:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Benford%27s_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBenford's Law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e states that the distribution of leading digits is not random. This is probably because many things grow logarithmically. Extract the leading digit from these vectors.\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 --\u0026gt; 1\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 --\u0026gt; 1\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0.3 --\u0026gt; 3\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4 --\u0026gt; 4\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-5 --\u0026gt; 5\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-0.006 --\u0026gt; 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput will be a vector\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 = [1 0.3 -2 0.001 -0.0006, 582398, 3020];]]\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\u003eOutput 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[ y = [1 3 2 1 6 5 3];]]\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":331,"title":"Compute Area from Fixed Sum Cumulative Probability","description":"In Matlab the code\r\n v = rand(1,3);\r\n v = v/sum(v);\r\nis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\r\n A = fixedsumarea(P);\r\nYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.","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: 311.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 155.65px; transform-origin: 407px 155.65px; 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: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn Matlab the code\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e v = rand(1,3);\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e v = v/sum(v);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; 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 73.5px; text-align: left; transform-origin: 384px 73.5px; 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: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\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: 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; \"\u003e A = fixedsumarea(P);\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: 362.5px 8px; transform-origin: 362.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = fixedsumarea(P)\r\n  P = 1/2;\r\n  A = 0;\r\nend","test_suite":"%%\r\nfiletext = fileread('fixedsumarea.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\nP = pi/4;\r\nA_correct = 0.7984235067141288;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = 1/sqrt(11);\r\nA_correct = 0.4964013344766580;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = exp(-3);\r\nA_correct = 0.1494793760894695;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = (1/27)^(1/5);\r\nA_correct = 0.6605992894366502;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = sin(sqrt(2));\r\nA_correct = 0.8634048022602919;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = 68/137;\r\nA_correct = 0.6471420329484348;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":28,"edited_by":223089,"edited_at":"2023-02-21T09:48:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-02-21T09:48:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-17T05:58:59.000Z","updated_at":"2026-08-06T09:03:06.000Z","published_at":"2012-02-17T18:47:40.000Z","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 Matlab the code\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[ v = rand(1,3);\\n v = v/sum(v);]]\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\u003eis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\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 = fixedsumarea(P);]]\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\u003eYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.\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":61446,"title":"Test your geometry knowledge!(simple)","description":"We have the following shape and you need to:\r\n1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\r\n2) Find the area of the semi-circle where DC is the diameter.(A_sc)\r\n3)Find the perimeter of the whole shape.(P_s)\r\n4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\r\n\r\nExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); 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: 551.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 275.9px; transform-origin: 469px 275.9px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe have the following shape and you need to:\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) Find the area of the semi-circle where DC is the diameter.(A_sc)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)Find the perimeter of the whole shape.(P_s)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 341.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 170.9px; text-align: left; transform-origin: 445px 170.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"630\" height=\"336\" style=\"vertical-align: baseline;width: 630px;height: 336px\" 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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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [A_tr A_sc P_s P_sc] = AREAS_AND_PERIMETERS(x,y)\r\n    \r\nend","test_suite":"%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(3, 4);\r\nassert(abs(a1 - 2.16) \u003c 1e-4);\r\nassert(abs(a2 - (9*pi/8)) \u003c 1e-4);\r\nassert(abs(p1 - (11 + 1.5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (3 + 1.5*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(6, 8);\r\nassert(abs(a1 - 8.64) \u003c 1e-4);\r\nassert(abs(a2 - (9*pi/2)) \u003c 1e-4);\r\nassert(abs(p1 - (22 + 3*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (6 + 3*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(5, 12);\r\nassert(abs(a1 - (750/169)) \u003c 1e-4);\r\nassert(abs(a2 - (25*pi/8)) \u003c 1e-4);\r\nassert(abs(p1 - (29 + 2.5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (5 + 2.5*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(10, 10);\r\nassert(abs(a1 - 25) \u003c 1e-4);\r\nassert(abs(a2 - (25*pi/2)) \u003c 1e-4);\r\nassert(abs(p1 - (30 + 5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (10 + 5*pi)) \u003c 1e-4);\r\n\r\n%%\r\nfor i = 1:10\r\n    rx = rand() * 99 + 1;\r\n    ry = rand() * 99 + 1;\r\n    \r\n    [a1, a2, p1, p2] = AREAS_AND_PERIMETERS(rx, ry);\r\n    \r\n    exp1 = (rx^3 * ry) / (2 * (rx^2 + ry^2));\r\n    exp2 = (pi * rx^2) / 8;\r\n    exp3 = rx + 2*ry + (pi * rx)/2;\r\n    exp4 = rx + (pi * rx)/2;\r\n    \r\n    assert(abs(a1 - exp1) \u003c 1e-4);\r\n    assert(abs(a2 - exp2) \u003c 1e-4);\r\n    assert(abs(p1 - exp3) \u003c 1e-4);\r\n    assert(abs(p2 - exp4) \u003c 1e-4);\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-23T12:02:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":0,"test_suite_updated_at":"2026-08-23T11:59:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-23T10:40:32.000Z","updated_at":"2026-08-23T12:02:47.000Z","published_at":"2026-08-23T11:59:11.000Z","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 have the following shape and you need to:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Find the area of the semi-circle where DC is the diameter.(A_sc)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)Find the perimeter of the whole shape.(P_s)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"336\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"630\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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20]]\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":43479,"title":"Modulation index","description":"The amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.","description_html":"\u003cp\u003eThe amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.\u003c/p\u003e","function_template":"function z = your_fcn_name(x,y)\r\n  z = ;\r\nend","test_suite":"%%\r\nx = 8; y=2;\r\nz_correct = 4;\r\nassert(isequal(your_fcn_name(x,y),z_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":87885,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-11T22:34:12.000Z","updated_at":"2026-02-06T15:38:09.000Z","published_at":"2016-10-11T22:34:12.000Z","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\u003eThe amplitude of the carrier signal is 2V and the amplitude of the modulating signal is 8V. Find its modulation index.\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":43033,"title":"Create a constant offset.","description":"Add a constant offset to an array.\r\n\r\nExample\r\n\r\n a = [1 3 5 9]\r\n offset = 2\r\n y = [3 5 7 11]","description_html":"\u003cp\u003eAdd a constant offset to an array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e a = [1 3 5 9]\r\n offset = 2\r\n y = [3 5 7 11]\u003c/pre\u003e","function_template":"function y = constant_offset(a,offset)\r\n  y = a;\r\nend","test_suite":"%%\r\na = 1;\r\noffset = 2\r\ny_correct = 3;\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n\r\n%%\r\na = [-1 1];\r\noffset = 2\r\ny_correct = [1 3];\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n\r\n%%\r\na = [-10:1:1];\r\noffset = 10\r\ny_correct = [0:11];\r\nassert(isequal(constant_offset(a,offset),y_correct))\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":0,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":136,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T08:20:41.000Z","updated_at":"2026-04-22T17:38:49.000Z","published_at":"2016-10-05T08:20:41.000Z","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\u003eAdd a constant offset to an array.\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\u003eExample\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 = [1 3 5 9]\\n offset = 2\\n y = [3 5 7 11]]]\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":2378,"title":"Area of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n  A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1005,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-08-14T17:22:23.000Z","published_at":"2014-06-18T17:40:40.000Z","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\u003eA triangle is given with base\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\u003e'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\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\u003e'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\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":45430,"title":"Juego de posiciones","description":"Crea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor. \r\n\r\nPor ejemplo:\r\n\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\n\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\n\r\nPD: Considerad el cero como número positivo. ","description_html":"\u003cp\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/p\u003e\u003cp\u003ePor ejemplo:\u003c/p\u003e\u003cp\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/p\u003e\u003cp\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/p\u003e\u003cp\u003ePD: Considerad el cero como número positivo.\u003c/p\u003e","function_template":"function x = order(y)\r\n \r\nend","test_suite":"%%\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\ny=[6 7 -34 9 0];\r\ny_correct= [-34 9 7 6 0];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":394942,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-09T11:48:17.000Z","updated_at":"2026-08-18T12:08:53.000Z","published_at":"2020-04-10T07:53:03.000Z","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\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePor ejemplo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [-1 6 15 -7 31 2 -4 -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\u003ey_correct = [-7 -5 -4 -1 31 15 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\u003ePD: Considerad el cero como número positivo.\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":45568,"title":"Times 5","description":"Try out this test problem first.\r\n\r\nGiven the variable x as your input, multiply it by five and put the result in y.\r\n\r\nExamples:\r\n\r\nInput  x = 1\r\n Output y is 5\r\n Input  x = 2\r\n Output y is 10","description_html":"\u003cp\u003eTry out this test problem first.\u003c/p\u003e\u003cp\u003eGiven the variable x as your input, multiply it by five and put the result in y.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003eInput  x = 1\r\n Output y is 5\r\n Input  x = 2\r\n Output y is 10\u003c/p\u003e","function_template":"function y = times5(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(times5(1),5));\r\n\r\n%%\r\nassert(isequal(times5(2),10));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":443529,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":119,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-21T15:30:36.000Z","updated_at":"2026-05-30T14:17:53.000Z","published_at":"2020-05-21T15:30:36.000Z","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\u003eTry out this test problem first.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 the variable x as your input, multiply it by five and put the result in 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput x = 1 Output y is 5 Input x = 2 Output y is 10\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":42986,"title":"Determine the roots of a cubic equation","description":"Given the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.","description_html":"\u003cp\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/p\u003e","function_template":"function y = cubicRoots(a,b,c,d)\r\n  y = [0 0 0];\r\nend","test_suite":"%%\r\na=1; b=3; c=3; d=1;\r\ny_correct = [-1 -1 -1];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=1; b=-6; c=11; d=-6;\r\ny_correct = [1 2 3];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=4; b=4; c=-1; d=-1;\r\ny_correct = [-1 -0.5 0.5];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":"2016-09-30T16:42:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:40:42.000Z","updated_at":"2026-05-28T15:58:44.000Z","published_at":"2016-09-16T10:40:42.000Z","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\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\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":1355,"title":"Given area find sides","description":"In a right angle triangle given area 'A' \r\none arm=x, another arm=2x\r\nthen find the value of x.\r\n\r\nFor example, area A=400 then x=20;","description_html":"\u003cp\u003eIn a right angle triangle given area 'A' \r\none arm=x, another arm=2x\r\nthen find the value of x.\u003c/p\u003e\u003cp\u003eFor example, area A=400 then x=20;\u003c/p\u003e","function_template":"function y = findside(A)\r\n  y = x+2x;\r\nend","test_suite":"%%\r\nA = 400;\r\ny_correct = 20;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 144;\r\ny_correct = 12;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 225;\r\ny_correct = 15;\r\nassert(isequal(findside(A),y_correct))\r\n\r\n%%\r\nA = 256;\r\ny_correct = 16;\r\nassert(isequal(findside(A),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":6975,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":567,"test_suite_updated_at":"2013-03-18T04:52:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-18T04:15:57.000Z","updated_at":"2026-07-28T18:16:54.000Z","published_at":"2013-03-18T04:23:49.000Z","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\u003eIn a right angle triangle given area 'A' one arm=x, another arm=2x then find the value of 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, area A=400 then x=20;\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":60321,"title":"Area of right triangle","description":"Given a hypotenuse and a leg , calculate the area of right triangle.","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 10.5px; transform-origin: 407.5px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a hypotenuse and a leg , calculate the area of right triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area(b,c)\r\n  y = b+c;\r\nend","test_suite":"%%\r\nb=4\r\nc=5\r\ny_correct = 6;\r\nassert(isequal(area(b,c),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4201661,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-15T21:08:41.000Z","updated_at":"2026-06-05T04:53:12.000Z","published_at":"2024-05-15T21:08:41.000Z","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:t\u003eGiven a hypotenuse and a leg , calculate the area of right triangle.\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":57725,"title":"Sequence problem","description":"find the nth term of the sequence:\r\n790\r\n1303\r\n2033\r\n____\r\n4366\r\n6095\r\n","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: 194.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.3125px; transform-origin: 407px 97.3125px; 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=\"\"\u003efind the nth term of the sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3125px; transform-origin: 391px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e790\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1303\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e2033\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"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\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4366\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6095\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sequence(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfunctions={'polyfit','polyval'};\r\nassessFunctionAbsence(functions, 'FileName', 'sequence.m');\r\n\r\n%%\r\nx = 1;\r\ny_correct = 790;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1303;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 6095;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 8293;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 18511;\r\nassert(isequal(sequence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2900827,"edited_by":2900827,"edited_at":"2023-02-20T05:07:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2023-02-20T05:07:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-19T16:34:33.000Z","updated_at":"2026-06-03T23:09:03.000Z","published_at":"2023-02-19T16:35:26.000Z","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\u003efind the nth term of the sequence:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e790\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1303\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc 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Possible Ruby Scores, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (Official NFL Scoring Plays). \r\nIn American football, the 7 possible ways of scoring are:\r\nTouchdown - 6 points\r\nTry after touchdown - 1 point\r\nTry after touchdown - 2 points\r\nSafety - 2 points\r\nField Goal - 3 points\r\nDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\r\nDefensive \"touchdown\" on try after touchdown - 2 points\r\nValues for score1 and score2 include all natural numbers (realistically \u003c100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\r\n*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by the opposing team.\r\nExample\r\n[t1_combs, t2_combs] = amerfootballscores(5, 8)\r\n\r\nt1_combs =\r\n\r\n     0     0     0     0     1     0     1\r\n     0     0     0     1     1     0     0\r\n     0     0     0     2     0     1     0\r\n\r\n\r\nt2_combs =\r\n\r\n     0     0     0     1     2     0     0\r\n     0     0     0     4     0     0     0\r\n     1     0     0     1     0     0     0\r\n     1     0     1     0     0     0     0\r\nThis system is known as a linear Diophantine equation, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\r\nEach team's score can be modeled by the following equation:\r\n6(tds) + 1(off. 1 pt. pats) + 2(off. 2 pt. pats) + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\r\n    \u003e\u003e\u003e with the added constraints:\r\n                off. 1 pt. pats + off. 2 pt. pats \u003c= tds\r\n                def. 1pt. pats + def. 2pt. pats \u003c= tds for opponent","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: 970.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 485.312px; transform-origin: 407px 485.312px; 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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWith inspiration from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56195-possible-rugby-scores\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56195. Possible Ruby Scores\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, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://operations.nfl.com/the-rules/nfl-video-rulebook/scoring-plays/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOfficial NFL Scoring Plays\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: 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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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 American football, the 7 possible ways of scoring are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTouchdown - 6 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTry after touchdown - 1 point\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTry after touchdown - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSafety - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eField Goal - 3 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDefensive \"touchdown\" on try after touchdown - 2 points\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eValues for score1 and score2 include all natural numbers (realistically \u0026lt;100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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-style: italic; \"\u003e*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by 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-style: italic; text-decoration: underline; text-decoration-line: underline; \"\u003eopposing team\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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-style: italic; \"\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 306.562px; 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 153.275px; transform-origin: 404px 153.281px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[t1_combs, t2_combs] = amerfootballscores(5, 8)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003et1_combs =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     0     1     0     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     1     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     2     0     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003et2_combs =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; 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: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     1     2     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     0     0     0     4     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1     0     0     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; 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: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; 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 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\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-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1     0     1     0     0     0     0\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-collapse: preserve; 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=\"\"\u003eThis system is known as a 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 equation\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, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach team's score can be modeled by the following equation:\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6(tds) + 1(off. 1 pt. pats) + 2\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 0.8px; border-bottom-style: solid; border-bottom-width: 0.8px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003eoff. 2 pt. pats\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 0.8px; border-bottom-style: solid; border-bottom-width: 0.8px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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    \u0026gt;\u0026gt;\u0026gt; with the added constraints:\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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                off. 1 pt. pats + off. 2 pt. pats \u0026lt;= tds\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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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                def. 1pt. pats + def. 2pt. pats \u0026lt;= tds for opponent\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t1_combs,t2_combs] = amerfootballscores(s1,s2)  \r\nt1_combs = [];  \r\nt2_combs = [];\r\n\r\nend","test_suite":"%%\r\ns1 = 5;\r\ns2 = 8;\r\nteam1 = [0     0     0     0     1     0     1;\r\n         0     0     0     1     1     0     0;\r\n         0     0     0     2     0     1     0];\r\nteam2 = [0     0     0     1     2     0     0;\r\n         0     0     0     4     0     0     0;\r\n         1     0     0     1     0     0     0;\r\n         1     0     1     0     0     0     0];\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\nassert(isequal([t1_combs;t2_combs],[team1;team2]))\r\n\r\n%%\r\ns1 = 0;\r\ns2 = 28;\r\nteam1 = [0     0     0     0     0     0     0];\r\nteam2 = [0     0     0     2     8     0     0;\r\n         0     0     0     5     6     0     0;\r\n         0     0     0     8     4     0     0;\r\n         0     0     0    11     2     0     0;\r\n         0     0     0    14     0     0     0;\r\n         1     0     0     2     6     0     0;\r\n         1     0     0     5     4     0     0;\r\n         1     0     0     8     2     0     0;\r\n         1     0     0    11     0     0     0;\r\n         1     0     1     1     6     0     0;\r\n         1     0     1     4     4     0     0;\r\n         1     0     1     7     2     0     0;\r\n         1     0     1    10     0     0     0;\r\n         1     1     0     0     7     0     0;\r\n         1     1     0     3     5     0     0;\r\n         1     1     0     6     3     0     0;\r\n         1     1     0     9     1     0     0;\r\n         2     0     0     2     4     0     0;\r\n         2     0     0     5     2     0     0;\r\n         2     0     0     8     0     0     0;\r\n         2     0     1     1     4     0     0;\r\n         2     0     1     4     2     0     0;\r\n         2     0     1     7     0     0     0;\r\n         2     0     2     0     4     0     0;\r\n         2     0     2     3     2     0     0;\r\n         2     0     2     6     0     0     0;\r\n         2     1     0     0     5     0     0;\r\n         2     1     0     3     3     0     0;\r\n         2     1     0     6     1     0     0;\r\n         2     1     1     2     3     0     0;\r\n         2     1     1     5     1     0     0;\r\n         2     2     0     1     4     0     0;\r\n         2     2     0     4     2     0     0;\r\n         2     2     0     7     0     0     0;\r\n         3     0     0     2     2     0     0;\r\n         3     0     0     5     0     0     0;\r\n         3     0     1     1     2     0     0;\r\n         3     0     1     4     0     0     0;\r\n         3     0     2     0     2     0     0;\r\n         3     0     2     3     0     0     0;\r\n         3     0     3     2     0     0     0;\r\n         3     1     0     0     3     0     0;\r\n         3     1     0     3     1     0     0;\r\n         3     1     1     2     1     0     0;\r\n         3     1     2     1     1     0     0;\r\n         3     2     0     1     2     0     0;\r\n         3     2     0     4     0     0     0;\r\n         3     2     1     0     2     0     0;\r\n         3     2     1     3     0     0     0;\r\n         3     3     0     2     1     0     0;\r\n         4     0     0     2     0     0     0;\r\n         4     0     1     1     0     0     0;\r\n         4     0     2     0     0     0     0;\r\n         4     1     0     0     1     0     0;\r\n         4     2     0     1     0     0     0;\r\n         4     2     1     0     0     0     0;\r\n         4     4     0     0     0     0     0];\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\nassert(isequal([t1_combs;t2_combs],[team1;team2]))\r\n\r\n%%\r\ns1 = 37;\r\ns2 = 49;\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\n% Matrices are rather large, so test case is dependent on the size of each output matrix, \r\n% where the number of rows will equate to the total number of scoring combinations\r\n[t1_rows,t1_cols] = size(t1_combs);\r\n[t2_rows,t2_cols] = size(t2_combs);\r\nassert(isequal([t1_rows,t2_rows],[2894,5625]))\r\n\r\n%%\r\ns1 = 37;\r\ns2 = 49;\r\n[t1_combs,t2_combs] = amerfootballscores(s1,s2);\r\n% Matrices are rather large, so test case is dependent on the sums of each column. These\r\n% values don't have any practical application.\r\nt1_sums = [6724, 2210, 1774, 10752, 6776, 7566, 5789];\r\nt2_sums = [19476, 6398, 5272, 28518, 18222, 11185, 9470];\r\nassert(isequal([t1_sums;t2_sums],[sum(t1_combs);sum(t2_combs)]))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":3499438,"edited_by":3499438,"edited_at":"2023-08-17T23:02:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-09T17:04:20.000Z","updated_at":"2026-06-04T20:28:24.000Z","published_at":"2023-08-10T05:17:56.000Z","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\u003eWith inspiration from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56195-possible-rugby-scores\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56195. Possible Ruby Scores\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, given the final score for two teams in an American football game (score1, score2), return two matrices (team1_combs, team2_combs) representing all possible combinations of scores by each team (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://operations.nfl.com/the-rules/nfl-video-rulebook/scoring-plays/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOfficial NFL Scoring Plays\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:t\u003eIn American football, the 7 possible ways of scoring are:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTouchdown - 6 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry after touchdown - 1 point\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry after touchdown - 2 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSafety - 2 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eField Goal - 3 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefensive safety on try after touchdown (i.e. conversion safety) - 1 points\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefensive \\\"touchdown\\\" on try after touchdown - 2 points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValues for score1 and score2 include all natural numbers (realistically \u0026lt;100), and the resulting matrices will have dimensions n1 x 7 and n2 x 7, where n1, n2 are the total number of possible scoring combinations for each team, respectively. The order of the elements in the rows for team1_combs and team2_combs should follow the above list.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e*** Attention - There is added complexity in the scoring possibilities in that the number of tries after touchdowns (also known as extra points or point after attempts) must be less than or equal to number of touchdowns. This constraint is further complicated by the possibility of defensive scores on tries after touchdowns, in which the possible number of scores is constrained by the touchdowns scored by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eopposing team\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\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[[t1_combs, t2_combs] = amerfootballscores(5, 8)\\n\\nt1_combs =\\n\\n     0     0     0     0     1     0     1\\n     0     0     0     1     1     0     0\\n     0     0     0     2     0     1     0\\n\\n\\nt2_combs =\\n\\n     0     0     0     1     2     0     0\\n     0     0     0     4     0     0     0\\n     1     0     0     1     0     0     0\\n     1     0     1     0     0     0     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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis system is known as a 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 equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, an equation where only the integer--and in this case only nonnegative--solutions are of interest.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach team's score can be modeled by the following equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6(tds) + 1(off. 1 pt. pats) + 2(off. 2 pt. pats) + 2(safs) + 3(fgs) + 1(def. 1 pt. pats) + 2(def. 2 pt. pats) = score\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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    \u0026gt;\u0026gt;\u0026gt; with the added constraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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                off. 1 pt. pats + off. 2 pt. pats \u0026lt;= tds\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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                def. 1pt. pats + def. 2pt. pats \u0026lt;= tds for opponent\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":47,"title":"Extract leading non-zero digit","description":"\u003chttp://en.wikipedia.org/wiki/Benford%27s_law Benford's Law\u003e states that the distribution of leading digits is not random.  This is probably because many things grow logarithmically.  Extract the leading digit from these vectors.\r\n\r\n* 10 --\u003e 1 \r\n* 13 --\u003e 1 \r\n* 0.3 --\u003e 3\r\n* -4 --\u003e 4 \r\n* -5 --\u003e 5 \r\n* -0.006 --\u003e 6\r\n\r\nInput will be a vector\r\n\r\n x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];\r\n\r\nOutput should be\r\n\r\n y = [1 3 2 1 6 5 3];\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Benford%27s_law\"\u003eBenford's Law\u003c/a\u003e states that the distribution of leading digits is not random.  This is probably because many things grow logarithmically.  Extract the leading digit from these vectors.\u003c/p\u003e\u003cul\u003e\u003cli\u003e10 --\u003e 1\u003c/li\u003e\u003cli\u003e13 --\u003e 1\u003c/li\u003e\u003cli\u003e0.3 --\u003e 3\u003c/li\u003e\u003cli\u003e-4 --\u003e 4\u003c/li\u003e\u003cli\u003e-5 --\u003e 5\u003c/li\u003e\u003cli\u003e-0.006 --\u003e 6\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eInput will be a vector\u003c/p\u003e\u003cpre\u003e x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];\u003c/pre\u003e\u003cp\u003eOutput should be\u003c/p\u003e\u003cpre\u003e y = [1 3 2 1 6 5 3];\u003c/pre\u003e","function_template":"function y = leadingDigit(x)\r\n  y = x\r\nend","test_suite":"%%\r\nx = [100 23 -34 0.005 -0.466664 -0.555 1 134534];\r\ny_correct = [1 2 3 5 4 5 1 1];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [57 -0.2 8913 -63 0.838127];\r\ny_correct = [5 2 8 6 8];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [-0.4336    0.3426    3.5784    2.7694   -1.3499];\r\ny_correct = [4 3 3 2 1];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n\r\n%%\r\nx = [0.3000 -0.1 -0.00000002 0.5 0.002];\r\ny_correct = [3 1 2 5 2];\r\nassert(isequal(leadingDigit(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":5,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2256,"test_suite_updated_at":"2012-05-29T14:34:23.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:23.000Z","updated_at":"2026-08-15T02:28:08.000Z","published_at":"2012-01-18T01:00:23.000Z","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:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Benford%27s_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBenford's Law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e states that the distribution of leading digits is not random. This is probably because many things grow logarithmically. Extract the leading digit from these vectors.\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 --\u0026gt; 1\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 --\u0026gt; 1\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0.3 --\u0026gt; 3\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4 --\u0026gt; 4\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-5 --\u0026gt; 5\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-0.006 --\u0026gt; 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput will be a vector\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 = [1 0.3 -2 0.001 -0.0006, 582398, 3020];]]\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\u003eOutput 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[ y = [1 3 2 1 6 5 3];]]\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":331,"title":"Compute Area from Fixed Sum Cumulative Probability","description":"In Matlab the code\r\n v = rand(1,3);\r\n v = v/sum(v);\r\nis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\r\n A = fixedsumarea(P);\r\nYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.","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: 311.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 155.65px; transform-origin: 407px 155.65px; 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: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn Matlab the code\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e v = rand(1,3);\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e v = v/sum(v);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; 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 73.5px; text-align: left; transform-origin: 384px 73.5px; 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: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\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: 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; \"\u003e A = fixedsumarea(P);\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: 362.5px 8px; transform-origin: 362.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = fixedsumarea(P)\r\n  P = 1/2;\r\n  A = 0;\r\nend","test_suite":"%%\r\nfiletext = fileread('fixedsumarea.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\nP = pi/4;\r\nA_correct = 0.7984235067141288;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = 1/sqrt(11);\r\nA_correct = 0.4964013344766580;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = exp(-3);\r\nA_correct = 0.1494793760894695;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = (1/27)^(1/5);\r\nA_correct = 0.6605992894366502;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = sin(sqrt(2));\r\nA_correct = 0.8634048022602919;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n%%\r\nP = 68/137;\r\nA_correct = 0.6471420329484348;\r\nassert(abs(fixedsumarea(P)-A_correct)\u003c100*eps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":28,"edited_by":223089,"edited_at":"2023-02-21T09:48:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-02-21T09:48:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-17T05:58:59.000Z","updated_at":"2026-08-06T09:03:06.000Z","published_at":"2012-02-17T18:47:40.000Z","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 Matlab the code\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[ v = rand(1,3);\\n v = v/sum(v);]]\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\u003eis sometimes suggested as a convenient means of generating three random variables, whose ranges are restricted to [0,1], which have a fixed sum of one. However, this procedure has the property that the area-wise density distribution of the three values, considered as cartesian coordinates in 3D space, is widely variable throughout the planar region of possible locations of v. For any given density value in the range of this density distribution, let A be the corresponding area of the subregion of all points whose density is less than or equal to this given value, and let P be the corresponding probability that v would lie in this subregion. The task is to write a function 'fixedsumarea' which receives P as an input and gives A as an output:\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 = fixedsumarea(P);]]\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\u003eYou should assume that initially 'rand(1,3)' perfectly generates three independent random variables each uniformly distributed on [0,1], but subsequently each is modified by being divided by their mutual sum.\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":61446,"title":"Test your geometry knowledge!(simple)","description":"We have the following shape and you need to:\r\n1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\r\n2) Find the area of the semi-circle where DC is the diameter.(A_sc)\r\n3)Find the perimeter of the whole shape.(P_s)\r\n4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\r\n\r\nExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); 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: 551.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 275.9px; transform-origin: 469px 275.9px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe have the following shape and you need to:\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) Find the area of the semi-circle where DC is the diameter.(A_sc)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)Find the perimeter of the whole shape.(P_s)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 341.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 170.9px; text-align: left; transform-origin: 445px 170.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"630\" height=\"336\" style=\"vertical-align: baseline;width: 630px;height: 336px\" 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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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [A_tr A_sc P_s P_sc] = AREAS_AND_PERIMETERS(x,y)\r\n    \r\nend","test_suite":"%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(3, 4);\r\nassert(abs(a1 - 2.16) \u003c 1e-4);\r\nassert(abs(a2 - (9*pi/8)) \u003c 1e-4);\r\nassert(abs(p1 - (11 + 1.5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (3 + 1.5*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(6, 8);\r\nassert(abs(a1 - 8.64) \u003c 1e-4);\r\nassert(abs(a2 - (9*pi/2)) \u003c 1e-4);\r\nassert(abs(p1 - (22 + 3*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (6 + 3*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(5, 12);\r\nassert(abs(a1 - (750/169)) \u003c 1e-4);\r\nassert(abs(a2 - (25*pi/8)) \u003c 1e-4);\r\nassert(abs(p1 - (29 + 2.5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (5 + 2.5*pi)) \u003c 1e-4);\r\n\r\n%%\r\n[a1, a2, p1, p2] = AREAS_AND_PERIMETERS(10, 10);\r\nassert(abs(a1 - 25) \u003c 1e-4);\r\nassert(abs(a2 - (25*pi/2)) \u003c 1e-4);\r\nassert(abs(p1 - (30 + 5*pi)) \u003c 1e-4);\r\nassert(abs(p2 - (10 + 5*pi)) \u003c 1e-4);\r\n\r\n%%\r\nfor i = 1:10\r\n    rx = rand() * 99 + 1;\r\n    ry = rand() * 99 + 1;\r\n    \r\n    [a1, a2, p1, p2] = AREAS_AND_PERIMETERS(rx, ry);\r\n    \r\n    exp1 = (rx^3 * ry) / (2 * (rx^2 + ry^2));\r\n    exp2 = (pi * rx^2) / 8;\r\n    exp3 = rx + 2*ry + (pi * rx)/2;\r\n    exp4 = rx + (pi * rx)/2;\r\n    \r\n    assert(abs(a1 - exp1) \u003c 1e-4);\r\n    assert(abs(a2 - exp2) \u003c 1e-4);\r\n    assert(abs(p1 - exp3) \u003c 1e-4);\r\n    assert(abs(p2 - exp4) \u003c 1e-4);\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-23T12:02:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":0,"test_suite_updated_at":"2026-08-23T11:59:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-23T10:40:32.000Z","updated_at":"2026-08-23T12:02:47.000Z","published_at":"2026-08-23T11:59:11.000Z","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 have the following shape and you need to:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Find the area of the triangle ABE(A_tr). (Suppose that the angle E is 90 degrees.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Find the area of the semi-circle where DC is the diameter.(A_sc)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)Find the perimeter of the whole shape.(P_s)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)Find the perimeter of the semi circle if we separate it from the whole shape(P_sc).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"336\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"630\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation if you are confused: x is the length and y is the width of the rectangle ABCDA and they will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[{"value":"Cody 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