Problem 2652. Kurchan 5x5 - 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 Problems 1646 and 2650, but bigger. Technically, all you need to do for this Cody problem is input a 5x5 matrix containing the numbers 1-25. 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(5) is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 17 24 1 8 15\n 23 5 7 14 16\n 4 6 13 20 22\n 10 12 19 21 3\n 11 18 25 2 9]]></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>17 * 24 * 1 * 8 * 15=48960</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>23 * 5 * 7 * 14 * 16=180320</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 * 6 * 13 * 20 * 22=137280</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>10 * 12 * 19 * 21 * 3=143640</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>11 * 18 * 25 * 2 * 9=89100</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>17 * 23 * 4 * 10 * 11=172040</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>24 * 5 * 6 * 12 * 18=155520</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>1 * 7 * 13 * 19 * 25=43225</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>8 * 14 * 20 * 21 * 2=94080</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>15 * 16 * 22 * 3 * 9=142560</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>17*5*13*21*9=208845</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>24*7*20*3*11=110880</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>1*14*22*10*18=55440</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>8*16*4*12*25=153600</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>15*23*6*19*2=78660</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>15*14*13*12*11=360360</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>8*7*6*10*9=30240</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>1*5*4*3*2=120</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>24*23*22*21*25=6375600</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>17*16*20*19*18=1860480</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 6375600, while the lowest is 120. Therefore, the score of this matrix is 6375480. 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 Problems 1646 and 2650, but bigger. Technically, all you need to do for this Cody problem is input a 5x5 matrix containing the numbers 1-25. 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(5) is<pre> 17 24 1 8 15
 23 5 7 14 16
 4 6 13 20 22
 10 12 19 21 3
 11 18 25 2 9</pre>The row products are:<ul><li>17 * 24 * 1 * 8 * 15=48960</li><li>23 * 5 * 7 * 14 * 16=180320</li><li>4 * 6 * 13 * 20 * 22=137280</li><li>10 * 12 * 19 * 21 * 3=143640</li><li>11 * 18 * 25 * 2 * 9=89100</li></ul>The column products are:<ul><li>17 * 23 * 4 * 10 * 11=172040</li><li>24 * 5 * 6 * 12 * 18=155520</li><li>1 * 7 * 13 * 19 * 25=43225</li><li>8 * 14 * 20 * 21 * 2=94080</li><li>15 * 16 * 22 * 3 * 9=142560</li></ul>The diagonal products are:<ul><li>17*5*13*21*9=208845</li><li>24*7*20*3*11=110880</li><li>1*14*22*10*18=55440</li><li>8*16*4*12*25=153600</li><li>15*23*6*19*2=78660</li></ul>The anti-diagonal products are:<ul><li>15*14*13*12*11=360360</li><li>8*7*6*10*9=30240</li><li>1*5*4*3*2=120</li><li>24*23*22*21*25=6375600</li><li>17*16*20*19*18=1860480</li></ul>The highest value is 6375600, while the lowest is 120. Therefore, the score of this matrix is 6375480. Your Cody score will be the Kurchan score of your matrix.

Related to Problems 1646 and 2650, but bigger. Technically, all you need to do for this Cody problem is input a 5x5 matrix containing the numbers 1-25. 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(5) is

17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

The row products are:

* 17 * 24 *  1 *  8 * 15=48960
* 23 *  5 *  7 * 14 * 16=180320
*  4 *  6 * 13 * 20 * 22=137280
* 10 * 12 * 19 * 21 *  3=143640
* 11 * 18 * 25 *  2 *  9=89100

The column products are:

*  17 * 23 *  4 * 10 * 11=172040
*  24 *  5 *  6 * 12 * 18=155520
*   1 *  7 * 13 * 19 * 25=43225
*   8 * 14 * 20 * 21 *  2=94080
*  15 * 16 * 22 *  3 *  9=142560

The diagonal products are:

* 17*5*13*21*9=208845
* 24*7*20*3*11=110880
* 1*14*22*10*18=55440
* 8*16*4*12*25=153600
* 15*23*6*19*2=78660

The anti-diagonal products are:

* 15*14*13*12*11=360360
* 8*7*6*10*9=30240
* 1*5*4*3*2=120
* 24*23*22*21*25=6375600
* 17*16*20*19*18=1860480

The highest value is 6375600, while the lowest is 120. Therefore, the score of this matrix is 6375480. Your Cody score will be the Kurchan score of your matrix.

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42 Solutions
25 Solvers

Last Solution submitted on Apr 23, 2021

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Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 21 Jul 2020

I went for the minimum score that I was able to find at least, and
found 102810. Moreover, I submitted the algorithm and the hardcoded solution.

Solution Comments

Solution 2719824

1 Comment

1 Comment

Rafael S.T. Vieira on 21 Jul 2020

Here, it is the algorithm to find my solution.

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