Problem 780. Give a matrix that matches itself when rotated

Created by Ned Gulley

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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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)

Problem 780. Give a matrix that matches itself when rotated

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6 solvers submitted 22 solutions (3.67 solutions/solver).

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