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Sudoku

 Sudoku

Mathieu Ledru

April 23, 2006
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  1. Sudoku
    5 3 7
    6 1 9 5
    9 8 6
    8 6 3
    4 8 3 1
    7 2 6
    6 2 8
    4 1 9 5
    8 7 9
    23-04-2006 @matyo91

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  2. Introduction


    Rules


    Solve methods


    Variants


    Media and Competitions
    Table of contents
    @matyo91
    @matyo91
    23-04-2006

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  3. Introduction
    @matyo91
    23-04-2006

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  4. Su means 'number'


    Doku means 'single'


    The digits must remain single
    Sudoku
    @matyo91
    @matyo91
    23-04-2006

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  5. 1707 Leonhard Euler


    1979 Howard Garns


    1984 Nikoli


    1989 Loadstar and Softdisk


    2005 Publishing in France
    History
    @matyo91
    @matyo91
    23-04-2006

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  6. Rules
    @matyo91
    23-04-2006

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  7. Ancestor : Latin square
    @matyo91
    @matyo91
    Latin square are N*N size
    1 2
    2 1
    1 2 3
    2 3 1
    3 1 2
    1 2 3 4
    4 3 2 1
    2 1 4 3
    3 4 1 2
    1 2 3 4 5
    4 5 1 2 3
    2 3 4 5 1
    5 1 2 3 4
    3 4 5 1 2
    1 2 3 4 5 6
    2 3 4 5 6 1
    3 4 5 6 1 2
    4 5 6 1 2 3
    5 6 1 2 3 4
    6 1 2 3 4 5
    1 2 3 4 5 6 7
    5 6 7 1 2 3 4
    2 3 4 5 6 7 1
    6 7 1 2 3 4 5
    3 4 5 6 7 1 2
    7 1 2 3 4 5 6
    4 5 6 7 1 2 3
    23-04-2006

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  8. Ancestor : Latin square
    @matyo91
    @matyo91
    Rule one : Every row must include all digits


    from 1 through n in any order
    1 2
    2 1
    1 2 3
    2 3 1
    3 1 2
    1 2 3 4
    4 3 2 1
    2 1 4 3
    3 4 1 2
    1 2 3 4 5
    4 5 1 2 3
    2 3 4 5 1
    5 1 2 3 4
    3 4 5 1 2
    1 2 3 4 5 6
    2 3 4 5 6 1
    3 4 5 6 1 2
    4 5 6 1 2 3
    5 6 1 2 3 4
    6 1 2 3 4 5
    1 2 3 4 5 6 7
    5 6 7 1 2 3 4
    2 3 4 5 6 7 1
    6 7 1 2 3 4 5
    3 4 5 6 7 1 2
    7 1 2 3 4 5 6
    4 5 6 7 1 2 3
    23-04-2006

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  9. Ancestor : Latin square
    @matyo91
    @matyo91
    Rule two : Every column must include all digits

    from 1 through n in any order
    1 2
    2 1
    1 2 3
    2 3 1
    3 1 2
    1 2 3 4
    4 3 2 1
    2 1 4 3
    3 4 1 2
    1 2 3 4 5
    4 5 1 2 3
    2 3 4 5 1
    5 1 2 3 4
    3 4 5 1 2
    1 2 3 4 5 6
    2 3 4 5 6 1
    3 4 5 6 1 2
    4 5 6 1 2 3
    5 6 1 2 3 4
    6 1 2 3 4 5
    1 2 3 4 5 6 7
    5 6 7 1 2 3 4
    2 3 4 5 6 7 1
    6 7 1 2 3 4 5
    3 4 5 6 7 1 2
    7 1 2 3 4 5 6
    4 5 6 7 1 2 3
    23-04-2006

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  10. @matyo91
    Sudoku
    The size of a grid is 9x9 square
    7 4 1 6 9 8 3 2 5
    5 3 8 2 4 1 6 7 9
    9 2 6 3 7 5 4 1 8
    4 1 3 8 2 6 9 5 7
    2 6 7 5 3 9 8 4 1
    8 5 9 4 1 7 2 3 6
    1 9 2 7 8 3 5 6 4
    3 7 5 9 6 4 1 8 2
    6 8 4 1 5 2 7 9 3
    23-04-2006

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  11. @matyo91
    Sudoku
    Sudoku has the same two first rules as Latin square
    7 4 1 6 9 8 3 2 5
    5 3 8 2 4 1 6 7 9
    9 2 6 3 7 5 4 1 8
    4 1 3 8 2 6 9 5 7
    2 6 7 5 3 9 8 4 1
    8 5 9 4 1 7 2 3 6
    1 9 2 7 8 3 5 6 4
    3 7 5 9 6 4 1 8 2
    6 8 4 1 5 2 7 9 3
    23-04-2006

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  12. @matyo91
    Sudoku
    Sudoku adds a third rule : Every 3 by 3 subsection of the 9 by 9
    square must include all digits from1 through 9
    7 4 1 6 9 8 3 2 5
    5 3 8 2 4 1 6 7 9
    9 2 6 3 7 5 4 1 8
    4 1 3 8 2 6 9 5 7
    2 6 7 5 3 9 8 4 1
    8 5 9 4 1 7 2 3 6
    1 9 2 7 8 3 5 6 4
    3 7 5 9 6 4 1 8 2
    6 8 4 1 5 2 7 9 3
    23-04-2006

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  13. @matyo91
    How many?
    All Latin Squares of size 3
    1 2 3
    2 3 1
    3 1 2
    1 2 3
    3 1 2
    2 3 1
    1 3 2
    2 1 3
    3 2 1
    1 3 2
    3 2 1
    2 1 3
    2 1 3
    1 3 2
    3 2 1
    2 1 3
    3 2 1
    1 3 2
    2 3 1
    1 2 3
    3 1 2
    2 3 1
    3 1 2
    1 2 3
    3 2 1
    1 3 2
    2 1 3
    3 2 1
    2 1 3
    1 3 2
    3 1 2
    1 2 3
    2 3 1
    3 1 2
    2 3 1
    1 2 3
    23-04-2006

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  14. @matyo91
    How many?
    Reduced Latin Squares of size 3
    1 2 3
    2 3 1
    3 1 2
    1 2 3
    3 1 2
    2 3 1
    1 3 2
    2 1 3
    3 2 1
    1 3 2
    3 2 1
    2 1 3
    2 1 3
    1 3 2
    3 2 1
    2 1 3
    3 2 1
    1 3 2
    2 3 1
    1 2 3
    3 1 2
    2 3 1
    3 1 2
    1 2 3
    3 2 1
    1 3 2
    2 1 3
    3 2 1
    2 1 3
    1 3 2
    3 1 2
    1 2 3
    2 3 1
    3 1 2
    2 3 1
    1 2 3
    23-04-2006

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  15. @matyo91
    How many?
    Reduced Latin Squares of size 3
    n Reduced Latin squares of size n All Latin squares of size n
    3 1 12
    6 9408 812851200
    9 377597570964259000 5524751496156890000000000000
    SUDOKU 5 472 730 538 6 670 903 752 021 072 936 960
    23-04-2006

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  16. Solve methods
    @matyo91
    23-04-2006

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  17. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 9 6 1
    1 2 3 4 5 6 7 8 9

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  18. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 9 6 1
    1 2 3 4 5 6 7 8 9

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  19. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 9 6 1
    1 2 3 4 5 6 7 8 9

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  20. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 9 6 1
    1 2 3 4 5 6 7 8 9

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  21. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1
    1 2 3 4 5 6 7 8 9

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  22. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1
    1?

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  23. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1

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  24. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1

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  25. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1

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  26. @matyo91
    Solve
    Only choice rule
    23-04-2006
    9 5 1 6 2
    6 4 5 1
    1 2 5 6 3 9 7 4
    2 5 8 4 7 6 3
    4 6 5 1 7
    8 7 6 1 2 5
    5 6 1 7 3 2 4 8
    1 2 9 7 6
    7 4 2 9 6 1

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  27. Variants
    @matyo91
    23-04-2006

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  28. @matyo91
    23-04-2006
    3 4
    2 6 1
    1 9 8 2
    5 6
    2 1
    9 8
    8 3 4 6
    4 1 9
    5 7

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  29. @matyo91
    23-04-2006
    5 9 6 3
    2 8 1
    7 9
    8 1 2 7 6
    4 3 5 4
    3 4 5
    3 5 7 3 1
    5 6 9 5 6
    1 3 2 4 9
    4 3 9
    8 1 2 5
    7 9 8 2
    7 1
    3 8 9
    1 2 7 4

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  30. Media and Competitions
    @matyo91
    23-04-2006

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  31. @matyo91
    23-04-2006

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  32. Hello!


    I Am Mathieu Ledru
    You can contact me at @matyo91
    @matyo91
    Thanks!
    Any questions?
    23-04-2006

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