Solving and constructing various types of sudoku tables using mathematical tools

Document Type : Review Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan

2 Department of Applied Mathematics, Faculty of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran

Abstract

Sudoku is a popular puzzle game worldwide and serves as a useful tool for children's education. In this article, we aim to explore the relationship between mathematics and various types of Sudoku tables. To achieve this, we first present a method based on integer programming optimization for solving the standard Sudoku table. Then, we extend this method to solve several other types of Sudoku tables. Finally, using mathematical techniques, we propose methods for constructing Sudoku tables.

Keywords

References

[1] S. E. Bammel and J. Rothstein, The number of 9 × 9 Latin squares, Discrete Math., 11 (1975) 93–95.
[2] A. C. Bartlett, T. P. Chartier, A. N. Langville and T. D. Rankin, An integer programming model for the Sudoku problem, J. of Online Mathematics and its Applications, 8 (2008) pp. 15.
[3] B. Berman, Sudoku-type gaming activity, KING SHOW GAMES Inc, U. S. Patent Application, 2008.
[4] M. J. Chlond, Classroom exercises in IP modeling: Su doku and the log pile, INFORMS Transactions on Education, 5 (2005) 77–79.
[5] J. P. Delahaye, The science behind Sudoku, Scientific American, 294 (2006) 80–87.
[6] R. DeVenezia, J. Garlach, L. Hoyle, T. Katz and R. Langston, SASr and Sudoku, SAS Global Forum, (2007), http://www2.sas.com/proceedings/forum2007/011-2007.pdf.
[7] G. McGuire, B. Tugemann and G. Civario, There is no 16-clue Sudoku: Solving the Sudoku minimum number of clues problem via hitting set enumeration, Experimental Mathematics, 23 (2014) 190–217.
[8] J. W. Morrow, , R. F. Marsden, M. A. Hein and R. A. Luciano, Bally Gaming Inc, (2007). Sudoku-type wagering game and method. U.S. Patent Application 11/626,224.
[9] Royle, G. Minimum Sudoku. http://www.csse.uwa.edu.au/~gordon/sudokumin.php.
[10] E. Russell and F. Jarvis, There are 5472730538 essentially different Sudoku grids · · · and the Sudoku symmetry group, http://www.afjarvis.staff.shef.ac.uk/sudoku/sudgroup.html.
[11] F. H. Simons, Solving a sudoku puzzle with mathematica, Mathematica in Education and Research, 10 (2005) 1–24.
[12] B. Torrence, Sudoku Game” from The Wolfram Demonstrations Project, (2011), http://demonstrations. wolfram.com/, SudokuGame.
[13] H. Yu, Y. Tang and C. Zong, Solving odd even sudoku puzzles by binary integer linear programming, In Natural
Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2016 12th International Conference on (2016) (2226–2230). IEEE.
[14] H. J. Weiss and R. A. Rasmussen, Lessons from modeling sudoku in excel, INFORMS Transactions on Education,
7) (2007) 178–184.
[15] Wikipedia, Sudoku solving algorithms-Wikipedia, The Free Encyclopedia [Online], Available: http://en.wikipedia.org/wiki/Sudokusolvingalgorithms.
Mathematics and Society
Volume 4, Issue 3 - Serial Number 3
September 2019
Pages 45-60

Files

Share

How to cite

Statistics