Problem 44334. Sums of Multiple Pairs of Triangular Numbers

Created by James

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This is a follow-up to Problem 44289 - Find two triangular numbers whose sum is input.

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:

 [ 3   15  36 
  78   66  45]

Good luck!

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Last Solution submitted on Jul 02, 2020

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1 Comment

Rafael S.T. Vieira on 2 Jul 2020 at 2:28

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.

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cody5 triangular numbers

Problem 44334. Sums of Multiple Pairs of Triangular Numbers

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Problem 44334. Sums of Multiple Pairs of Triangular Numbers

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