Problem 2650. Kurchan 4x4 - Optimal score

Created by James

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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>Related to Problem 1646, but bigger. Technically, all you need to do for this Cody problem is input a 4x4 matrix containing the numbers 1-16. However, your score will be the Kurchan value of the matrix, which is defined as the difference between the maximum and minimum of the products for the rows, columns, diagonals, and anti-diagonals of the matrix.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example: Magic(4) is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 16 2 3 13\n 5 11 10 8\n 9 7 6 12\n 4 14 15 1]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The row products are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>16*2*3*13=1248</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>5*11*10*8=4400</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>9*7*6*12=4536</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>4*14*15*1=840</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The column products are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>16*9*5*4=2880</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>2*11*7*14=2156</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>3*10*6*15=2700</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>13*8*12*1=1248</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The diagonal products are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>16*11*6*1=1056</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>2*10*12*4=960</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>3*8*9*14=3024</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>13*5*7*15=6825</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The anti-diagonal products are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>13*10*7*4=3640</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>3*11*9*1=297</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>2*5*12*15=1800</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>16*8*6*14=10752</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The highest value is 10752, while the lowest is 297. Therefore, the score of this matrix is 10455. Your Cody score will be the Kurchan score of your matrix.</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>"}]}

Related to Problem 1646, but bigger. Technically, all you need to do for this Cody problem is input a 4x4 matrix containing the numbers 1-16. However, your score will be the Kurchan value of the matrix, which is defined as the difference between the maximum and minimum of the products for the rows, columns, diagonals, and anti-diagonals of the matrix.For example: Magic(4) is<pre> 16 2 3 13
 5 11 10 8
 9 7 6 12
 4 14 15 1</pre>The row products are:<ul><li>16*2*3*13=1248</li><li>5*11*10*8=4400</li><li>9*7*6*12=4536</li><li>4*14*15*1=840</li></ul>The column products are:<ul><li>16*9*5*4=2880</li><li>2*11*7*14=2156</li><li>3*10*6*15=2700</li><li>13*8*12*1=1248</li></ul>The diagonal products are:<ul><li>16*11*6*1=1056</li><li>2*10*12*4=960</li><li>3*8*9*14=3024</li><li>13*5*7*15=6825</li></ul>The anti-diagonal products are:<ul><li>13*10*7*4=3640</li><li>3*11*9*1=297</li><li>2*5*12*15=1800</li><li>16*8*6*14=10752</li></ul>The highest value is 10752, while the lowest is 297. Therefore, the score of this matrix is 10455. Your Cody score will be the Kurchan score of your matrix.

Related to Problem 1646, but bigger.  Technically, all you need to do for this Cody problem is input a 4x4 matrix containing the numbers 1-16.  However, your score will be the Kurchan value of the matrix, which is defined as the difference between the maximum and minimum of the products for the rows, columns, diagonals, and anti-diagonals of the matrix.

For example: Magic(4) is

16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1

The row products are:

* 16*2*3*13=1248
* 5*11*10*8=4400
* 9*7*6*12=4536
* 4*14*15*1=840

The column products are:

* 16*9*5*4=2880
* 2*11*7*14=2156
* 3*10*6*15=2700
* 13*8*12*1=1248

The diagonal products are:

* 16*11*6*1=1056
* 2*10*12*4=960
* 3*8*9*14=3024
* 13*5*7*15=6825

The anti-diagonal products are:

* 13*10*7*4=3640
* 3*11*9*1=297
* 2*5*12*15=1800
* 16*8*6*14=10752

The highest value is 10752, while the lowest is 297.  Therefore, the score of this matrix is 10455.  Your Cody score will be the Kurchan score of your matrix.

Solve

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Last Solution submitted on Oct 26, 2022

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Rafael S.T. Vieira on 21 Jul 2020

And do we seek to obtain a higher or lower score? what is the goal?

Rafael S.T. Vieira on 21 Jul 2020

I went for the minimum score that I was able to find at least, and
found 3724. Moreover, I submitted the algorithm and the hardcoded solution.

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Solution 2719818

1 Comment

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Rafael S.T. Vieira on 21 Jul 2020

Here, it is the algorithm to find my solution.

Solution 519012

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1 Comment

James on 31 Oct 2014

Worst Possible Passing Score. :-)

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Problem 2650. Kurchan 4x4 - Optimal score

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Problem 2650. Kurchan 4x4 - Optimal score

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