Sudoku Info

Board cell numbering:

0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18                
27                
36                
45                
54                
63                
72 73 74 75 76 77 78 79 80

 

Cliques:

A "clique" (my term) is a list of the 9 cells that have to contain the numbers 1 through 9.  for instance, the to row is a clique: [0,1,2,3,4,5,6,7,8], as is the first column: [0,9,18,27,36,45,54,63,72].  There are 27cliques -- each row, each column and each square.  Here are all the cliques:

Cliques=[[0,1,2,3,4,5,6,7,8],\
[9,10,11,12,13,14,15,16,17],\
[18,19,20,21,22,23,24,25,26],\
[27,28,29,30,31,32,33,34,35],\
[36,37,38,39,40,41,42,43,44],\
[45,46,47,48,49,50,51,52,53],\
[54,55,56,57,58,59,60,61,62],\
[63,64,65,66,67,68,69,70,71],\
[72,73,74,75,76,77,78,79,80],\
[0,9,18,27,36,45,54,63,72],\
[1,10,19,28,37,46,55,64,73],\
[2,11,20,29,38,47,56,65,74],\
[3,12,21,30,39,48,57,66,75],\
[4,13,22,31,40,49,58,67,76],\
[5,14,23,32,41,50,59,68,77],\
[6,15,24,33,42,51,60,69,78],\
[7,16,25,34,43,52,61,70,79],\
[8,17,26,35,44,53,62,71,80],\
[0,1,2,9,10,11,18,19,20],\
[3,4,5,12,13,14,21,22,23],\
[6,7,8,15,16,17,24,25,26],\
[27,28,29,36,37,38,45,46,47],\
[30,31,32,39,40,41,48,49,50],\
[33,34,35,42,43,44,51,52,53],\
[54,55,56,63,64,65,72,73,74],\
[57,58,59,66,67,68,75,76,77],\
[60,61,62,69,70,71,78,79,80]\
]

 

The Neighbors dictionary: the key is the cell number, and the value is a list of all the "neighbors" of that cell, namely those cells which MUST have values different from the key cell's value.

Neighbors = {\
0: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 27, 36, 45, 54, 63, 72],\
1: [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 28, 37, 46, 55, 64, 73],\
2: [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 29, 38, 47, 56, 65, 74],\
3: [0, 1, 2, 4, 5, 6, 7, 8, 12, 13, 14, 21, 22, 23, 30, 39, 48, 57, 66, 75],\
4: [0, 1, 2, 3, 5, 6, 7, 8, 12, 13, 14, 21, 22, 23, 31, 40, 49, 58, 67, 76],\
5: [0, 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 22, 23, 32, 41, 50, 59, 68, 77],\
6: [0, 1, 2, 3, 4, 5, 7, 8, 15, 16, 17, 24, 25, 26, 33, 42, 51, 60, 69, 78],\
7: [0, 1, 2, 3, 4, 5, 6, 8, 15, 16, 17, 24, 25, 26, 34, 43, 52, 61, 70, 79],\
8: [0, 1, 2, 3, 4, 5, 6, 7, 15, 16, 17, 24, 25, 26, 35, 44, 53, 62, 71, 80],\
9: [0, 1, 2, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 36, 45, 54, 63, 72],\
10: [0, 1, 2, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 28, 37, 46, 55, 64, 73],\
11: [0, 1, 2, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 29, 38, 47, 56, 65, 74],\
12: [3, 4, 5, 9, 10, 11, 13, 14, 15, 16, 17, 21, 22, 23, 30, 39, 48, 57, 66, 75],\
13: [3, 4, 5, 9, 10, 11, 12, 14, 15, 16, 17, 21, 22, 23, 31, 40, 49, 58, 67, 76],\
14: [3, 4, 5, 9, 10, 11, 12, 13, 15, 16, 17, 21, 22, 23, 32, 41, 50, 59, 68, 77],\
15: [6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 26, 33, 42, 51, 60, 69, 78],\
16: [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 26, 34, 43, 52, 61, 70, 79],\
17: [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 35, 44, 53, 62, 71, 80],\
18: [0, 1, 2, 9, 10, 11, 19, 20, 21, 22, 23, 24, 25, 26, 27, 36, 45, 54, 63, 72],\
19: [0, 1, 2, 9, 10, 11, 18, 20, 21, 22, 23, 24, 25, 26, 28, 37, 46, 55, 64, 73],\
20: [0, 1, 2, 9, 10, 11, 18, 19, 21, 22, 23, 24, 25, 26, 29, 38, 47, 56, 65, 74],\
21: [3, 4, 5, 12, 13, 14, 18, 19, 20, 22, 23, 24, 25, 26, 30, 39, 48, 57, 66, 75],\
22: [3, 4, 5, 12, 13, 14, 18, 19, 20, 21, 23, 24, 25, 26, 31, 40, 49, 58, 67, 76],\
23: [3, 4, 5, 12, 13, 14, 18, 19, 20, 21, 22, 24, 25, 26, 32, 41, 50, 59, 68, 77],\
24: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 33, 42, 51, 60, 69, 78],\
25: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 34, 43, 52, 61, 70, 79],\
26: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 44, 53, 62, 71, 80],\
27: [0, 9, 18, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 54, 63, 72],\
28: [1, 10, 19, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 55, 64, 73],\
29: [2, 11, 20, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 56, 65, 74],\
30: [3, 12, 21, 27, 28, 29, 31, 32, 33, 34, 35, 39, 40, 41, 48, 49, 50, 57, 66, 75],\
31: [4, 13, 22, 27, 28, 29, 30, 32, 33, 34, 35, 39, 40, 41, 48, 49, 50, 58, 67, 76],\
32: [5, 14, 23, 27, 28, 29, 30, 31, 33, 34, 35, 39, 40, 41, 48, 49, 50, 59, 68, 77],\
33: [6, 15, 24, 27, 28, 29, 30, 31, 32, 34, 35, 42, 43, 44, 51, 52, 53, 60, 69, 78],\
34: [7, 16, 25, 27, 28, 29, 30, 31, 32, 33, 35, 42, 43, 44, 51, 52, 53, 61, 70, 79],\
35: [8, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 42, 43, 44, 51, 52, 53, 62, 71, 80],\
36: [0, 9, 18, 27, 28, 29, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 54, 63, 72],\
37: [1, 10, 19, 27, 28, 29, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 55, 64, 73],\
38: [2, 11, 20, 27, 28, 29, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 56, 65, 74],\
39: [3, 12, 21, 30, 31, 32, 36, 37, 38, 40, 41, 42, 43, 44, 48, 49, 50, 57, 66, 75],\
40: [4, 13, 22, 30, 31, 32, 36, 37, 38, 39, 41, 42, 43, 44, 48, 49, 50, 58, 67, 76],\
41: [5, 14, 23, 30, 31, 32, 36, 37, 38, 39, 40, 42, 43, 44, 48, 49, 50, 59, 68, 77],\
42: [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78],\
43: [7, 16, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 51, 52, 53, 61, 70, 79],\
44: [8, 17, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 51, 52, 53, 62, 71, 80],\
45: [0, 9, 18, 27, 28, 29, 36, 37, 38, 46, 47, 48, 49, 50, 51, 52, 53, 54, 63, 72],\
46: [1, 10, 19, 27, 28, 29, 36, 37, 38, 45, 47, 48, 49, 50, 51, 52, 53, 55, 64, 73],\
47: [2, 11, 20, 27, 28, 29, 36, 37, 38, 45, 46, 48, 49, 50, 51, 52, 53, 56, 65, 74],\
48: [3, 12, 21, 30, 31, 32, 39, 40, 41, 45, 46, 47, 49, 50, 51, 52, 53, 57, 66, 75],\
49: [4, 13, 22, 30, 31, 32, 39, 40, 41, 45, 46, 47, 48, 50, 51, 52, 53, 58, 67, 76],\
50: [5, 14, 23, 30, 31, 32, 39, 40, 41, 45, 46, 47, 48, 49, 51, 52, 53, 59, 68, 77],\
51: [6, 15, 24, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 60, 69, 78],\
52: [7, 16, 25, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 61, 70, 79],\
53: [8, 17, 26, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 62, 71, 80],\
54: [0, 9, 18, 27, 36, 45, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],\
55: [1, 10, 19, 28, 37, 46, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],\
56: [2, 11, 20, 29, 38, 47, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],\
57: [3, 12, 21, 30, 39, 48, 54, 55, 56, 58, 59, 60, 61, 62, 66, 67, 68, 75, 76, 77],\
58: [4, 13, 22, 31, 40, 49, 54, 55, 56, 57, 59, 60, 61, 62, 66, 67, 68, 75, 76, 77],\
59: [5, 14, 23, 32, 41, 50, 54, 55, 56, 57, 58, 60, 61, 62, 66, 67, 68, 75, 76, 77],\
60: [6, 15, 24, 33, 42, 51, 54, 55, 56, 57, 58, 59, 61, 62, 69, 70, 71, 78, 79, 80],\
61: [7, 16, 25, 34, 43, 52, 54, 55, 56, 57, 58, 59, 60, 62, 69, 70, 71, 78, 79, 80],\
62: [8, 17, 26, 35, 44, 53, 54, 55, 56, 57, 58, 59, 60, 61, 69, 70, 71, 78, 79, 80],\
63: [0, 9, 18, 27, 36, 45, 54, 55, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74],\
64: [1, 10, 19, 28, 37, 46, 54, 55, 56, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74],\
65: [2, 11, 20, 29, 38, 47, 54, 55, 56, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74],\
66: [3, 12, 21, 30, 39, 48, 57, 58, 59, 63, 64, 65, 67, 68, 69, 70, 71, 75, 76, 77],\
67: [4, 13, 22, 31, 40, 49, 57, 58, 59, 63, 64, 65, 66, 68, 69, 70, 71, 75, 76, 77],\
68: [5, 14, 23, 32, 41, 50, 57, 58, 59, 63, 64, 65, 66, 67, 69, 70, 71, 75, 76, 77],\
69: [6, 15, 24, 33, 42, 51, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 78, 79, 80],\
70: [7, 16, 25, 34, 43, 52, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 78, 79, 80],\
71: [8, 17, 26, 35, 44, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 78, 79, 80],\
72: [0, 9, 18, 27, 36, 45, 54, 55, 56, 63, 64, 65, 73, 74, 75, 76, 77, 78, 79, 80],\
73: [1, 10, 19, 28, 37, 46, 54, 55, 56, 63, 64, 65, 72, 74, 75, 76, 77, 78, 79, 80],\
74: [2, 11, 20, 29, 38, 47, 54, 55, 56, 63, 64, 65, 72, 73, 75, 76, 77, 78, 79, 80],\
75: [3, 12, 21, 30, 39, 48, 57, 58, 59, 66, 67, 68, 72, 73, 74, 76, 77, 78, 79, 80],\
76: [4, 13, 22, 31, 40, 49, 57, 58, 59, 66, 67, 68, 72, 73, 74, 75, 77, 78, 79, 80],\
77: [5, 14, 23, 32, 41, 50, 57, 58, 59, 66, 67, 68, 72, 73, 74, 75, 76, 78, 79, 80],\
78: [6, 15, 24, 33, 42, 51, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80],\
79: [7, 16, 25, 34, 43, 52, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80],\
80: [8, 17, 26, 35, 44, 53, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79]\
}