Problem 1646. Kurchan 3x3 - Optimal Score

Created by Richard Zapor

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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

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 used

The 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:* None

*Output:* Kurchan Square [3x3] that scores 198

I expect someone to give a min size hardcoded solution at some point.

Related Challenges:

1) <http://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function Kurchan Square Evaluation>

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 Challenge

5) Minimize Sum of Products (N=4:9) and a Large number Challenge

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Last Solution submitted on Nov 14, 2021

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Lincoln Poon on 21 Jan 2021

Yes. 198 is the best possible.

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Problem 1646. Kurchan 3x3 - Optimal Score

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Problem 1646. Kurchan 3x3 - Optimal Score

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