Problem 44334. Sums of Multiple Pairs of Triangular Numbers

Created by James

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This is a follow-up to</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44289\"><w:r><w:t>Problem 44289</w:t></w:r></w:hyperlink><w:r><w:t> - Find two triangular numbers whose sum is input.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There are some numbers that are the sum of multiple pairs of triangular numbers. For example, 81 = 36+45 = 15+66 = 3+78. Given a number X, find all of the possible pairs of triangular numbers that add up to X. Your answer should be in a 2-by-X matrix. Each column of the matrix should sum to X, and each pair of triangular numbers should only appear once. The top row sorted from low to high. The output for 81 would be:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ [ 3   15  36 \n  78   66  45]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Good luck!</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

731 Solutions
227 Solvers

Last Solution submitted on Jan 20, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 2 Jul 2020

The first test case is wrong 0 and 21 are triangular numbers too (https://oeis.org/A000217), therefore:
multi_triangular(21)
[ 0, 6;
21, 15]

PS: And 0 does not make a pair with every number in this case.

Solution Comments

Solution 1373096

2 Comments

2 Comments

Smith on 8 Dec 2017

What's wrong with the case x=20 in test suite? Why is y_correct=[ 10 10] ? I cannot pass it.

James on 11 Dec 2017

I don't know why your cheat isn't working, but look closely at what numbers your "for n=1:N" loop generates for that case.

Problem Recent Solvers227

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44334. Sums of Multiple Pairs of Triangular Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers227

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Problem 44334. Sums of Multiple Pairs of Triangular Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers227

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Players