數獨另ㄧ問 - 數獨
By Hamiltion
at 2008-04-13T23:12
at 2008-04-13T23:12
Table of Contents
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,6,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
(2,4) 8 3 | (1,4,9) 7 5 | (2,4) (1,2,6,9) (1,4,6)
先將能填入的數字都寫出來 如上圖
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,6,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
(2,4) 8 3 | (1,4,9) 7 5 | (2,4) (1,2,6,9) (1,4,6)
(1) 先看第七列的這兩個６
在左下的宮格中
只有這兩個地方可以放６
因此
這一列上其他的６必須刪除
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
A(2,4) 8 3 | (1,4,9) 7 5 | B(2,4) (1,2,6,9) (1,4,6)
(2) 接著是第九列的２和４
因為不是A=2,B=4就是A=4,B=2
因此
第九列其他的２和４
必須刪除
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
A(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) C(1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
B(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) D(1,4,7)
(2,4) 8 3 | (1,9) 7 5 | (2,4) (1,6,9) (1,6)
(3) 第一行的７剩下的A,B兩個位置
和第九行的７剩下的C,D兩個位置可以組成一個長方形
因為若A=7則D=7;若B=7則C=7
因此A,C所在的第二列以及B,D所在的第八列
其他的７必須刪除
(2,4,5) (3,4,5) B(1,2) | 7 6 9 | (2,3,4,5) 8 D(1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
(2,4,5,7) (4,5,9) A(2) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
C(2,4) 8 3 | (1,9) 7 5 | E(2,4) (1,6,9) (1,6)
(4-1) 之後可以填入的數字有 A=2 , B=1 , C=4 , D=4 , E=2
(2,5) (3,5) 1 | 7 6 9 | B(3,5) 8 4
(2,7) (3,4,6) 9 | 5 8 (1,2) | A(3) (1,2,6) (1,6,7)
8 (5,6) (6,7) | 3 4 (1,2) | C(5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (5,6,9) (6,7) | E(4,9) 2 8 | D(4,5,7) (5,9) 3
(5,7) (5,9) 2 |G(1,4,9) 3 6 | 8 (1,5,9) (1,7)
4 8 3 | F(1,9) 7 5 | 2 (1,6,9) (1,6)
(4-2) 之後可以填入的數字有 A=3 , B=5 , C=7 , D=4 , E=9 , F=1 , G=4
(2) (3) 1 | 7 6 9 | 5 8 4
(2,7) (4,6) 9 | 5 8 (1,2) | 3 (1,2,6) (1,6)
8 (5,6) (6) | 3 4 (1,2) | 7 (1,2,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (5,6) (6,7) | 9 2 8 | 4 (5) 3
(5,7) (5,9) 2 | 4 3 6 | 8 (1,5,9) (1,7)
4 8 3 | 1 7 5 | 2 (6,9) (6)
(4-3) 其他格的結果
2 3 1 7 6 9 5 8 4
7 4 9 5 8 2 3 6 1
8 5 6 3 4 1 7 2 9
3 1 5 8 9 4 6 7 2
6 7 8 2 1 3 9 4 5
9 2 4 6 5 7 1 3 8
1 6 7 9 2 8 4 5 3
5 9 2 4 3 6 8 1 7
4 8 3 1 7 5 2 9 6
這是答案
--
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,6,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
(2,4) 8 3 | (1,4,9) 7 5 | (2,4) (1,2,6,9) (1,4,6)
先將能填入的數字都寫出來 如上圖
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,6,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
(2,4) 8 3 | (1,4,9) 7 5 | (2,4) (1,2,6,9) (1,4,6)
(1) 先看第七列的這兩個６
在左下的宮格中
只有這兩個地方可以放６
因此
這一列上其他的６必須刪除
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
A(2,4) 8 3 | (1,4,9) 7 5 | B(2,4) (1,2,6,9) (1,4,6)
(2) 接著是第九列的２和４
因為不是A=2,B=4就是A=4,B=2
因此
第九列其他的２和４
必須刪除
(2,4,5) (3,4,5) (1,2) | 7 6 9 | (2,3,4,5) 8 (1,4)
A(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4,7) (1,2,6) C(1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
B(2,4,5,7) (4,5,9) (2,7) | (1,4,9) 3 6 | 8 (1,2,5,9) D(1,4,7)
(2,4) 8 3 | (1,9) 7 5 | (2,4) (1,6,9) (1,6)
(3) 第一行的７剩下的A,B兩個位置
和第九行的７剩下的C,D兩個位置可以組成一個長方形
因為若A=7則D=7;若B=7則C=7
因此A,C所在的第二列以及B,D所在的第八列
其他的７必須刪除
(2,4,5) (3,4,5) B(1,2) | 7 6 9 | (2,3,4,5) 8 D(1,4)
(2,4,7) (3,4,6) 9 | 5 8 (1,2) | (2,3,4) (1,2,6) (1,4,6,7)
8 (5,6) (1,2,6,7) | 3 4 (1,2) | (2,5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (4,5,6,9) (6,7) | (4,9) 2 8 | (4,5,7) (5,9) 3
(2,4,5,7) (4,5,9) A(2) | (1,4,9) 3 6 | 8 (1,2,5,9) (1,4,7)
C(2,4) 8 3 | (1,9) 7 5 | E(2,4) (1,6,9) (1,6)
(4-1) 之後可以填入的數字有 A=2 , B=1 , C=4 , D=4 , E=2
(2,5) (3,5) 1 | 7 6 9 | B(3,5) 8 4
(2,7) (3,4,6) 9 | 5 8 (1,2) | A(3) (1,2,6) (1,6,7)
8 (5,6) (6,7) | 3 4 (1,2) | C(5,7) (1,2,5,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (5,6,9) (6,7) | E(4,9) 2 8 | D(4,5,7) (5,9) 3
(5,7) (5,9) 2 |G(1,4,9) 3 6 | 8 (1,5,9) (1,7)
4 8 3 | F(1,9) 7 5 | 2 (1,6,9) (1,6)
(4-2) 之後可以填入的數字有 A=3 , B=5 , C=7 , D=4 , E=9 , F=1 , G=4
(2) (3) 1 | 7 6 9 | 5 8 4
(2,7) (4,6) 9 | 5 8 (1,2) | 3 (1,2,6) (1,6)
8 (5,6) (6) | 3 4 (1,2) | 7 (1,2,6) 9
------------------------------------------------------------------------------
3 1 5 | 8 9 4 | 6 7 2
6 7 8 | 2 1 3 | 9 4 5
9 2 4 | 6 5 7 | 1 3 8
------------------------------------------------------------------------------
1 (5,6) (6,7) | 9 2 8 | 4 (5) 3
(5,7) (5,9) 2 | 4 3 6 | 8 (1,5,9) (1,7)
4 8 3 | 1 7 5 | 2 (6,9) (6)
(4-3) 其他格的結果
2 3 1 7 6 9 5 8 4
7 4 9 5 8 2 3 6 1
8 5 6 3 4 1 7 2 9
3 1 5 8 9 4 6 7 2
6 7 8 2 1 3 9 4 5
9 2 4 6 5 7 1 3 8
1 6 7 9 2 8 4 5 3
5 9 2 4 3 6 8 1 7
4 8 3 1 7 5 2 9 6
這是答案
--
Tags:
數獨
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