Presentations

Event Title

Implications of Sudoku Boards as Matrices

Date

April 2021

Location

Online

Description

Sudoku boards consist of a 9 x 9 grid composed of nine 3 x 3 boxes that contain nine individual squares each. A valid Sudoku board consists of the integers 1 through 9 placed exactly once in each box, column, and row in the board. This study focuses on the 4 x 4 variants of Sudoku boards called Shidoku boards. The researcher treated Shidoku boards as matrices to examine patterns that produced determinants of zero. This study found that a Shidoku board with two repeated pairs of integers on its main diagonal is guaranteed to have a determinant of zero regardless of integer placement in the board. Additionally, the researcher conducted an exhaustive search of Shidoku board determinants and found that 160 out of all 288 possible Shidoku boards have determinants of zero. Furthermore, the researcher found that all 12 potential patterns for Shidoku boards produce at least eight determinants of zero under the permutations of 1, 2, 3, and 4. By addressing this topic in relation to Shidoku boards, this study will enhance the current literature on Shidoku and Sudoku boards with the hope of inspiring continued research on these boards as matrices.

Presentation Type

Presentation

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Implications of Sudoku Boards as Matrices

Online

Sudoku boards consist of a 9 x 9 grid composed of nine 3 x 3 boxes that contain nine individual squares each. A valid Sudoku board consists of the integers 1 through 9 placed exactly once in each box, column, and row in the board. This study focuses on the 4 x 4 variants of Sudoku boards called Shidoku boards. The researcher treated Shidoku boards as matrices to examine patterns that produced determinants of zero. This study found that a Shidoku board with two repeated pairs of integers on its main diagonal is guaranteed to have a determinant of zero regardless of integer placement in the board. Additionally, the researcher conducted an exhaustive search of Shidoku board determinants and found that 160 out of all 288 possible Shidoku boards have determinants of zero. Furthermore, the researcher found that all 12 potential patterns for Shidoku boards produce at least eight determinants of zero under the permutations of 1, 2, 3, and 4. By addressing this topic in relation to Shidoku boards, this study will enhance the current literature on Shidoku and Sudoku boards with the hope of inspiring continued research on these boards as matrices.