There is real mathematics in Sudoku

• Main Authors: Bersamina, Maisie T., Garde, Honeylyn A.
• 格式: text
• 語言: English
• 出版: Animo Repository 2008
• 主題: Sudoku; Puzzles
• 在線閱讀: https://animorepository.dlsu.edu.ph/etd_honors/282
• 機構: De La Salle University

This thesis is an exposition on the article Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes by R. A. Bailey, Peter J. Cameron, and Robert Connelly that appeared in the May 2008 issue of the American Mathematical Monthly. This discusses the significant interplay among various established fields of mathematics, such as Abstract and Linear Algebra, Design theory, Affine and Projective Geometry, and Coding theory, over Sudoku, one of the popular games in the 21s century. In Design theory, a Sudoku solution is characterized as a special case of a gerechte design, which is an n x n grid that is partitioned into n regions, each having n cells and that each of the symbols 1, ..., n is placed once in a row, once in a column, and once in a region. In Affine and Projective Geometry, the Sudoku board is coordinatized using the Galois field GF (3), and a set of partitions such as subsquares, broken rows , broken columns, and locations are introduced to constitute a special type of Sudoku solutions called symmetric. In Coding theory, the coordinatized Sudoku board is used in explaining the properties of the symmetric Sudoku solutions using the concepts of perfect 1-error-correcting codes. All of these noteworthy relationships among fields of mathematics contribute to the construction of sets of mutually orthogonal Sudoku solutions of maximum sizes.