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Sets of Mutually Orthogonal Sudoku Latin Squares

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A Latin square of order n is an n x n array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is called mutually orthogonal if when any pair of the squares are superimposed, the n2 ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9 symbols appears exactly once in each of the 3 by 3 blocks that together tile the main array. In response to a problem in the American Mathematical Monthly, we provide two constructions for mutually orthogonal Latin squares (MOLS) that are also solution to Sudoku puzzles. We generalize this notion from n = 9 to n = k2 and construct sets of mutually orthogonal Sudoku Latin squares (MOSLS) for any integer k>1 with a lower bound on the attainable size of such a set.
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Document Type: Research Article

Publication date: 2009-05-01

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