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COMMENTS
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A magic cube is the 3-dimensional equivalent of a magic square, that is, n^3 distinct integers arranged in an n X n X n grid such that the sum of the integers in each row, each column, each pillar, and the four main space diagonals is equal to the same number, called magic constant of the cube.
The magic cube is associative if the sum of any 2 numbers, symmetrically located relative to the center of the cube, is equal to the same number, called constant of associativity of the cube.
Magic cubes of order 3 are simple magic cubes.
All magic cubes of order 3 are associative.
The first two prime magic cubes of order 3 were found by Akio Suzuki in 1977 (see Prime Number Magic Cubes link).
The general formula of the magic cube of order 3:
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. x1, x2, 3k/2-x1-x2,
. x3, x4, 3k/2-x3-x4,
. 3k/2-x1-x3, 3k/2-x2-x4, -3k/2+x1+x2+x3+x4,
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. -k+x2+x3+x4, 2k-2*x2-x4, k/2+x2-x3,
. 2k-2*x3-x4, k/2, -k+2*x3+x4,
. k/2-x2+x3, -k+2*x2+x4, 2k-x2-x3-x4,
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. 5k/2-x1-x2-x3-x4, -k/2+x2+x4, -k/2+x1+x3,
. -k/2+x3+x4, k-x4, k-x3,
. -k/2+x1+x2, k-x2, k-x1
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Here k is the constant of associativity (any even number), x1, x2, x3, x4 are any integers.
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