Abstract
It turns out that it is always possible to make such a selection. The proof is a simple application of Hall's Marriage Theorem, as we show in Example 1 in the next section. In Sections 3 and 4, we identify winning the solitaire game with decomposing a semi-magic square into a linear combination, with positive integer coefficients, of permutation matrices. The remainder of the paper discusses the number of permutation matrices needed to express a given semi-magic square. 2. MARRIAGE. Suppose there are sets A1, A2,. .., An, and you wish to know whether there exist distinct objects xl, x2,.. . , x,, such that xl is in A1, x2 is in
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