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 c 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 = k[superscript 2] and construct sets of mutually orthogonal Sudoku Latin squares (MOSLS) for any integer k greater than 1 with a lower bound on the attainable size of such a set.