Problem 2652. Kurchan 5x5 - Optimal Score

Created by James

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>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.

Solve

Solution Stats

34 Solutions
33 Solvers

Last Solution submitted on Aug 27, 2020

Last 200 Solutions

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.

Problem Recent Solvers33

Problem Tags

Problem 2652. Kurchan 5x5 - Optimal Score

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author80

Problem Tags

Problem 2652. Kurchan 5x5 - Optimal Score

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author80

Problem Tags

Players