1. Sudoku

2. Introduction In this presentation I will cover the Sudoku puzzle, some basics of its complexity as well as specifically discussing the complexity of order 2 and order 3 Sudoku puzzles. I will also show and discuss the beginnings of NDFSMs for order 2 Sudoku puzzles and order 3 Sudoku puzzles to determine if a solution is correct.

3. Rules Most commonly, a sudoku puzzle is a 9x9 grid of the numbers 1-9 where in each row, column, and 3x3 grid each number is only used once. This is an “order 3” sudoku – an order n sudoku would be an n 2 xn 2 grid of the numbers 1-n, with n 2 nxn grids.

4. Example 73624 358 68475 5629 78 5629 73219 417 68154

5. Solution 157389624 324567981 968142375 873456219 492718563 516293748 735824196 249631857 681975432

6. How complex is it? For an order 3 sudoku you just have to be able to count to 9, so how hard are they really? How many different answers can there be?

7. Order 2 sudoku For order 2 sudoku puzzles there are 288 possible answers When symmetries are considered there are actually only 2 distinct puzzles with the remainder being some variation

8. Order 3 sudoku For order 3 sudoku puzzles there are 6,670,903,752,021,072,936,960 possible combinations Symmetrical operations only reduce this to 3,546,146,300,288

9. Beginnings of an order 2 DFSM

10. Basics of an order 3 DFSM

11. More complex data structure 2 dimensional array for checking – Number the columns, rows, and interior grids – Boolean 2 dimensional array for solving – Number the columns, rows, and interior grids – Each cell has a linked list of possible values – Some sort of relationship among the rows, columns, and grids to identify what cells are affected by a change in each

12. Conclusion If you can solve sudoku puzzles you’re a genius! Both a human or computer would take a different approach to solve or verify a solution, as FSMs are probably not the best way to approach the problem

13. References “A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles” J.F. Crook http://www.ams.org/notices/200904/tx09040 0460p.pdf http://www.ams.org/notices/200904/tx09040 0460p.pdf American Scientist “Unwed Numbers” Brian Hayes http://www.americanscientist.org/issues/issu e.aspx?id=3475&y=0&no=&content=true&pag e=4&css=print http://www.americanscientist.org/issues/issu e.aspx?id=3475&y=0&no=&content=true&pag e=4&css=print