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

Print

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

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