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]\
]