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Mathematics of Sudoku: Solving Techniques, Difficulty Degree, Graph Theory and Linear Algebraic Approach

Mosaheb, Rafieh | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49967 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahmoodian, Ebadollah
  7. Abstract:
  8. Sudoku is an intellectual game based on mathematics. Sudoku achieved global fame in a short time because this game doesn’t need any mathematical operation like addition and multiplication and in theory, instead of numbers, lechers, shapes,colors, etc. could be placed.Sudoku which is a single-player game in generally the player should complete a partial n2 × n2 matrix M all of whose enteries are drawn from {1; 2,..., n2} by applying the rules: no number may appear more than once in any row, any column,or any of the nine ‘‘blocks’’. Actually blocks are n × n submatrixs with indices {na + 1, na + 2,…, na + n} × {nb + 1, nb + 2,….., nb + n} Actually, A Sudoku is A Latin square with one additional rule: Numbers in blocks should be unique. According to global popularity of Sudoku puzzle, this puzzle has been studied academically in abundance. Now more than 310 research papers with subject Sudoku approves this sentence. chis thesis is a study on athematics of Sudoku: Topics like counting number of Sudoku puzzles, Sudoku trade and intercalate, assigning graph and hypergraph to Sudoku puzzle and coloring them, popular techniques for solving Sudoku puzzles, how to define the difficulty degree of Sudoku, and some interesting problems in Sudoku such as least number of clues in valid Sudoku.In addition, new results about intersection spectrum of two Shidokus and linear algebraic approach to Sudoku has presented
  9. Keywords:
  10. Sudoku ; Sudoku Graph ; Coloring ; Intercalate ; Trade ; Sudoku Hypergraph ; Difficalty Degree

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