Problem 1646. Kurchan 3x3 - Optimal Score

Created by Richard Zapor

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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>Find an optimal 3x3 Kurchan square, score of 198.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A 3x3 Kurchan square has values 1:9.The products of each row, column, diagonal, and anti-diagonal are used</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The Kurchan-value is the Max minus the Minimum of these products.</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>Example: m=[5 1 8;3 9 4;7 2 6]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Row Products: 40,108, and 84. Column products 105, 18, and 192.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Diagonal Products: 270, 1*4*7=28, and 8*3*2=48.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Anti-Diagonal Products: 8*9*7=504, 1*3*6=18, and 5*4*2=40.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>K is thus 504-18 = 486. [ Max of all products - Min of all products ]</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>Input:</w:t></w:r><w:r><w:t> None</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>Output:</w:t></w:r><w:r><w:t> Kurchan Square [3x3] that scores 198</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>I expect someone to give a min size hardcoded solution at some point.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Related Challenges:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>1)</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function\"><w:r><w:t>Kurchan Square Evaluation</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>2) Minimize Kurchan Squares (N=4:9)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>3) Minimize Kurchan Squares (N=10:20) [Very large numbers]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>4) Maximize Sum of Products (N=4:9) and a Large number Challenge</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>5) Minimize Sum of Products (N=4:9) and a Large number Challenge</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>"}]}

Find an optimal 3x3 Kurchan square, score of 198.A 3x3 Kurchan square has values 1:9.The products of each row, column, diagonal, and anti-diagonal are usedThe Kurchan-value is the Max minus the Minimum of these products.Example: m=[5 1 8;3 9 4;7 2 6]Row Products: 40,108, and 84. Column products 105, 18, and 192.Diagonal Products: 270, 1*4*7=28, and 8*3*2=48.Anti-Diagonal Products: 8*9*7=504, 1*3*6=18, and 5*4*2=40.K is thus 504-18 = 486. [ Max of all products - Min of all products ]Input: NoneOutput: Kurchan Square [3x3] that scores 198I expect someone to give a min size hardcoded solution at some point.Related Challenges:1) <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function">Kurchan Square Evaluation</a>2) Minimize Kurchan Squares (N=4:9)3) Minimize Kurchan Squares (N=10:20) [Very large numbers]4) Maximize Sum of Products (N=4:9) and a Large number Challenge5) Minimize Sum of Products (N=4:9) and a Large number Challenge

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