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Published byDennis Terry Modified over 9 years ago
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Magic square An example of how to represent a problem An idea from Chris Beck
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put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal
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Back to CP
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put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 1st stab Use sum(x) = sum(y) where x and y are - different rows - different columns - different diagonals Every element of the array is different - represent as a clique of not equals How does it go? For propagation and search?
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put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 2nd stab Use allDiff But what is k? How does model perform?
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Magic
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Could edit this
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Magic What is k?
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Magic Just a counter
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Magic S is actual square v is S flattened
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Magic Create S, its transpose TS and S flattened into v
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Magic That’s why we flattened S
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Magic Transpose is neat (thanks Neil Moore)
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Is this solution unique?
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Magic square on the web http://mathforum.org/alejandre/magic.square.html http://mathworld.wolfram.com/MagicSquare.html
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Is there an order 3 magic square with the number 5 in one of the outer corners?
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Thanks to Chris Beck
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