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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 44855 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Mahmoodian, Ebadollah
- Abstract:
- There are many fun plays and Sudoku is one of the most popular one. Although this game was published in 1979 for the first time as a puzzle in American magazine, it was published continuously from 1986 in Japan. This game has been known as an internationally popular game since 2005 and its national completion was held in Philadelphia. Sudoku had been considered as a hobby for several years before its mathematical importance was known in articles such as “Taking Sudoku seriously” and “The science behind Sudoku”. Using a lot of computer times, Gary McGuire et al in their article “There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem” found that the minimum number of filled cells required to solve a Sudoku is 17. Generalizing Sudoku (a table of n2 by n2 that includes n2 blocks with n cells and in each of its rows, columns and blocks has all numbers from 1 to n2 appeared once and only once). Since Sudoku has just one condition more than Latin square, we can discuss the problems of Latin square for Sudoku too and it seems that we can get better results because of the existence of one more condition. Latin square and its critical set are used in cryptography so Sudoku is expected to be used in this way too. In this thesis, we try to study problems raised in Sudoku mathematically and applications of Sudoku. The relationship between these problems and Latin square problems is considered too
- Keywords:
- Sudoku ; Latin Square Method ; Critical set
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