Problem 2160. The 17x17 Problem

Created by Ned Gulley

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{"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 problem is sometimes referred to as the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://bit-player.org/2009/the-17x17-challenge\"><w:r><w:t>17x17 challenge</w:t></w:r></w:hyperlink><w:r><w:t>. See also</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/512-spot-the-rectangle\"><w:r><w:t>Part 1</w:t></w:r></w:hyperlink><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2\"><w:r><w:t>Part 2</w:t></w:r></w:hyperlink><w:r><w:t> of this problem. This time, your job is to construct, for the given n, an n-by-n matrix in which there are no rectangles. A rectangle is a formed whenever four instances of the same value appear in the corners of a rectangular region of the matrix.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Examples:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ Input n = 3\n\n Output a = [ 4 1 2\n 1 4 3\n 2 1 1 ]\n\n Input n = 5\n Output a = [ 4 1 2 4 1\n 3 3 2 1 4\n 3 2 4 1 1\n 1 4 3 2 2\n 1 1 1 4 4 ]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The answer for a given n is not unique. The test suite will just guarantee that there are no rectangles present.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Note 1.</w:t></w:r><w:r><w:t> I am using Alfonso's</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2/solutions/191508\"><w:r><w:t>solution 191508</w:t></w:r></w:hyperlink><w:r><w:t> from</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2\"><w:r><w:t>problem 514</w:t></w:r></w:hyperlink><w:r><w:t> as my testing code. Cody in the service of Cody!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Note 2.</w:t></w:r><w:r><w:t> You can easily answer this problem with a pre-computed response. You could do that, but it would be lame. We want to see your code!</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>"}]}

This problem is sometimes referred to as the <a href = "http://bit-player.org/2009/the-17x17-challenge">17x17 challenge</a>. See also <a href = "http://www.mathworks.com/matlabcentral/cody/problems/512-spot-the-rectangle">Part 1</a> and <a href = "http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2">Part 2</a> of this problem. This time, your job is to construct, for the given n, an n-by-n matrix in which there are no rectangles. A rectangle is a formed whenever four instances of the same value appear in the corners of a rectangular region of the matrix.Examples:<pre> Input n = 3</pre><pre> Output a = [ 4 1 2
 1 4 3
 2 1 1 ]</pre><pre> Input n = 5
 Output a = [ 4 1 2 4 1
 3 3 2 1 4
 3 2 4 1 1
 1 4 3 2 2
 1 1 1 4 4 ]</pre>The answer for a given n is not unique. The test suite will just guarantee that there are no rectangles present.Note 1. I am using Alfonso's <a href = "http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2/solutions/191508">solution 191508</a> from <a href = "http://www.mathworks.com/matlabcentral/cody/problems/514-spot-the-rectangle-part-2">problem 514</a> as my testing code. Cody in the service of Cody!Note 2. You can easily answer this problem with a pre-computed response. You could do that, but it would be lame. We want to see your code!

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Ned Gulley on 3 Sep 2014

See Note 2 in the problem description.

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17x17 number theory

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Problem 2160. The 17x17 Problem

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