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Sudoku

Sudoku. Introduction.

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Sudoku

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  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 n2xn2 grid of the numbers 1-n, with n2 nxn grids.

  4. Example

  5. Solution

  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/tx090400460p.pdf • American Scientist “Unwed Numbers” Brian Hayes http://www.americanscientist.org/issues/issue.aspx?id=3475&y=0&no=&content=true&page=4&css=print

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