Sudoku

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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Introduction

Rules

Solve methods

Variants

Media and Competitions
Table of contents
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23-04-2006

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Introduction
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23-04-2006

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Su means 'number'

Doku means 'single'

The digits must remain single
Sudoku
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23-04-2006

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1707 Leonhard Euler

1979 Howard Garns

1984 Nikoli

1989 Loadstar and Softdisk

2005 Publishing in France
History
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23-04-2006

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Rules
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23-04-2006

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Ancestor : Latin square
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@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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@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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@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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@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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@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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@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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@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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@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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@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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Solve methods
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23-04-2006

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@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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@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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@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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@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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@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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Variants
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23-04-2006

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@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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@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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Media and Competitions
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23-04-2006

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@matyo91
23-04-2006

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Hello!

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

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Sudoku

Sudoku

Mathieu Ledru

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