Solving Puzzles ( Eg . Sudoku ) and Other Combinatorial Problems with Sat

There are many combinatorial puzzles around the world. Solving these puzzles is an intellectual challenge to human kinds. In computing, one way of solving these combinatorial puzzles is by modeling them as a satisfiablility problem (SAT). The SAT problem is to find given a propositional logic formula an assignment of the variables which makes the formula true. In this project, we use Sudoku, the Japan originated combinatorial puzzle, as the “play yard” for experiment on SAT modeling and current SAT solver technology evaluation. In this paper, we demonstrate the relationship between human logic rule and CNF resolution. As a result, SAT problem can be used to find practical rule in combinatorial problems. In the rest of paper, higher dimension Sudoku and Sudoku variations are modeled and examined using existing SAT solvers. At the end, basic SAT algorithms are used for examine the efficiency of different modeling of a given problem.