There is real mathematics in Sudoku
Date of Publication
2008
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics with specialization in Business Applications
College
College of Science
Department/Unit
Mathematics and Statistics
Honor/Award
Awarded as best thesis, 2008
Thesis Adviser
Arlene A. Pascasio
Defense Panel Chair
Blessilda P. Raposa
Defense Panel Member
Jose Tristan F. Reyes
Edmundo R. Perez
Abstract/Summary
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.
Abstract Format
html
Language
English
Format
Accession Number
TU15410
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
1 v. (various foliations) : ill. (some col.) ; 28 cm.
Keywords
Sudoku; Puzzles
Recommended Citation
Bersamina, M. T., & Garde, H. A. (2008). There is real mathematics in Sudoku. Retrieved from https://animorepository.dlsu.edu.ph/etd_honors/282