Sudoku Puzzles by using x-wing techniques

The purpose of this essay is to implement and study different techniques for solving Sudoku puzzles, a problem similar to graph coloring with fixed size and dependencies. Three approaches are presented and compared regarding efficiency (time needed, space required and success rate). These approaches are rule-based solving, simulated annealing, and searching for solutions. Finally the parts found to be most important for an efficient solver are combined, creating an even better solve. Sudoku puzzles involve a lot of mathematics. Of course, the puzzles are filled with numbers, but the solution process would be the same regardless of the symbols used. More interesting is the logic behind the solution process, which can provide extra satisfaction upon solving a puzzle (with a lot less erasing). In addition, the puzzles are examples of Latin squares?important in abstract algebra and in statis- tics, in experimental design.