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Mathieu Ledru
April 23, 2006
Education
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Mathieu Ledru
April 23, 2006
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Transcript
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
Introduction Rules Solve methods Variants Media and Competitions Table of
contents @matyo91 @matyo91 23-04-2006
Introduction @matyo91 23-04-2006
Su means 'number' Doku means 'single' The digits must remain
single Sudoku @matyo91 @matyo91 23-04-2006
1707 Leonhard Euler 1979 Howard Garns 1984 Nikoli 1989 Loadstar
and Softdisk 2005 Publishing in France History @matyo91 @matyo91 23-04-2006
Rules @matyo91 23-04-2006
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
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
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
@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
@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
@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
@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
@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
@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
Solve methods @matyo91 23-04-2006
@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
@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
@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
@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
@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
@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?
@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
@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
@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
@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
Variants @matyo91 23-04-2006
@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
@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
Media and Competitions @matyo91 23-04-2006
@matyo91 23-04-2006
Hello! I Am Mathieu Ledru You can contact me at
@matyo91 @matyo91 Thanks! Any questions? 23-04-2006
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