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Semimagic Square


A semimagic square is a square that fails to be a magic square only because one or both of the main diagonal sums do not equal the magic constant (Kraitchik 1942, p. 143). Note some care with terminology is necessary. For example, Jelliss terms a semimagic square a "magic square" and a magic square a "diagonally magic square."

SemimagicSquares

The number of distinct semimagic squares (treating squares differing by rotations and reflections as identical) of orders 1, 2, ... are 1, 0, 8, .... The eight semimagic squares of order 3 are illustrated above.


See also

Franklin Magic Square, Magic Square

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References

Update a linkJelliss, G. "Knight's Tour Notes." http://home.freeuk.net/ktn/Update a linkJelliss, G. "General Theory of Magic Knight's Tours." http://home.freeuk.net/ktn/mg.htmKraitchik, M. Mathematical Recreations. New York: W. W. Norton, 1942.

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Semimagic Square

Cite this as:

Weisstein, Eric W. "Semimagic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemimagicSquare.html

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