**ERIC Number:**EJ862225

**Record Type:**Journal

**Publication Date:**2009-May

**Pages:**7

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0746-8342

Sets of Mutually Orthogonal Sudoku Latin Squares

Vis, Timothy; Petersen, Ryan M.

College Mathematics Journal, v40 n3 p174-180 May 2009

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.

Descriptors: Problem Solving, Mathematics Instruction, College Mathematics, Games, Symbols (Mathematics), Mathematical Concepts

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A