Semi-magic squares, permutation matrices and constant line-sum matrices

This thesis is based mainly on Sections 1 to 6 of the article entitled Marriage, Magic and Solitaire by David Leep and Gerry Myerson (1999). Motivated by a non-losing solitaire game, the main part of this thesis begins by explaining how the Hall's Marriage Theorem applies to the solitaire game. It proceeds by approaching the solitaire game problem from the point of view of semi-magic squares. This approach provides a second way of proving the solitaire game. This is followed up with a discussion of permutation matrices, the simplest nonzero semi-magic squares. This thesis proves a theorem concerning permutation matrices as building blocks of semi-magic squares. Finally, the concept of permutation matrices and semi-magic squares is generalized to constant line-sum matrices over an arbitrary field.