Problem 780. Give a matrix that matches itself when rotated

Created by Ned Gulley

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>Given n and s, return a n-by-n matrix a of integers such that</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ sum(sum(a == rot90(a)))]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>is equal to exactly s. The integers should be chosen from the set 1 to n.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So for instance, if n is 2, and s is 2, you could return</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ a = [ 1 1 \n       2 2 ]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>since rot90(a) matches a in exactly one place.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For any n and s, a is of course not unique. I'm only checking to make sure the conditions are true.</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

30 Solutions
19 Solvers

Last Solution submitted on Jun 12, 2020

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

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?

Solution Comments

Solution 163139

1 Comment

1 Comment

Khaled Hamed on 16 Nov 2012

Just Tweaking...

Problem Recent Solvers19

Problem Tags

matrix manipulation

Problem 780. Give a matrix that matches itself when rotated

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author49

Problem Tags

Problem 780. Give a matrix that matches itself when rotated

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author49

Problem Tags

Players