Sudoku

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# Sudoku - PowerPoint PPT Presentation

Sudoku. Introduction.

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## PowerPoint Slideshow about ' Sudoku' - harley

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Presentation Transcript

### Sudoku

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.
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.
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?
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
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
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
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
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