Problem 780. Give a matrix that matches itself when rotated

Ned Gulley

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Given n and s, return a n-by-n matrix a of integers such that

 sum(sum(a == rot90(a)))

is equal to exactly s. The integers should be chosen from the set 1 to n.

So for instance, if n is 2, and s is 2, you could return

 a = [ 1 1 
       2 2 ]

since rot90(a) matches a in exactly one place.

For any n and s, a is of course not unique. I'm only checking to make sure the conditions are true.

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42 Solutions

13 Solvers

Last Solution submitted on Feb 04, 2025

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James on 16 Nov 2012

In the problem description, you say "The integers should be chosen from the set 1 to n." However, in your example for a 2x2 matrix, you have a 3 as one of the terms. Am I missing something?

Richard Zapor on 16 Nov 2012

function a = match_rot(n)
The problem says given n and s.
However, only n is provided.
Are we allowed to set s?

Richard Zapor on 16 Nov 2012

s=feval(@evalin,'caller','s');

Lack of s input solved

Ned Gulley on 16 Nov 2012

Sorry guys. Sloppy problem creation on my part. Unfortunately my signature change will invalidate all the solutions up to this point, but yes it should be match_rot(n,s)

David Verrelli on 1 Dec 2017

"since rot90(a) matches a in exactly _two_ places" for the example in the problem statement?

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