The number of "magic" squares and hypercubes

Details The number of "magic" squares and hypercubes The number of "magic" squares and hypercubes

2002-01-02

arxiv.org/abs/math/0201013v3

American Mathematical Monthly 110, no. 8 (2003), 707-717

Mathematics

Combinatorics

11 pages, 2 figures

Scientific paper

We define a magic square to be a square matrix whose entries are nonnegative
integers and whose rows, columns, and main diagonals sum up to the same number.
We prove structural results for the number of such squares as a function of the
size of the matrix and the line sum. We give examples for small sizes and show
similar results for symmetric, pandiagonal magic squares, and magic hypercubes.

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