关键词: 数独, 智力游戏, 推理性质, 唯一解, 算法性质

Abstract: It began with the requirement of Sudoku to establish the system of equations. The solution of equation system was equivalent to the original Sudoku. And many mathematical properties were derived from equation system, including candidates elimination techniques, unique determination property, contradiction property and invariance property. It also illustrated that the artificial deductive rules included these properties. Finally this paper proposed a algorithm which calculated the solution of equation system from these properties. The algorithm used a three-dimensional matrix to express the candidate matrix of an unsolved Sudoku, and according to the above properties the candidate matrix could be deleted until Sudoku was solved. The algorithm can resolve many difficult Sudoku puzzles. Two difficult Sudoku puzzles were demonstrated and solved easily with the method in this paper, which shows the method is very effective.

Key words: Sudoku, intelligent game, deductive character, unique solution, algorithm character