SudokuWiki.org
Strategies for Popular Number Puzzles
Killer Combinations
Each clue in each cage will give rise to a certain set of combinations of numbers for each cell. It is a convention of Killer Sudoku that no cage will duplicate a number (even if it dog-legs through several 3 by 3 boxes).
Some cages will not be very helpful but certain combinations, such as these listed here mean that the total number of possible numbers is equal to the cage size. In the first, for example, a clue of 3 in a cage of size 2 can only have 1 and 2 in it. These means you can remove 3 to 9 from those cells.
I have written an example of the use of 'hard' Killer combinations on this page.
Some cages will not be very helpful but certain combinations, such as these listed here mean that the total number of possible numbers is equal to the cage size. In the first, for example, a clue of 3 in a cage of size 2 can only have 1 and 2 in it. These means you can remove 3 to 9 from those cells.
I have written an example of the use of 'hard' Killer combinations on this page.
| Clue | Cage Size | Combinations |
| 3 | 2 | 1,2 |
| 4 | 2 | 1,3 |
| 16 | 2 | 7,9 |
| 17 | 2 | 8,9 |
| 6 | 3 | 1,2,3 |
| 7 | 3 | 1,2,4 |
| 23 | 3 | 6,8,9 |
| 24 | 3 | 7,8,9 |
| 10 | 4 | 1,2,3,4 |
| 11 | 4 | 1,2,3,5 |
| 29 | 4 | 5,7,8,9 |
| 30 | 4 | 6,7,8,9 |
| 15 | 5 | 1,2,3,4,5 |
| 16 | 5 | 1,2,3,4,6 |
| 34 | 5 | 4,6,7,8,9 |
| 35 | 5 | 5,6,7,8,9 |
| 21 | 6 | 1,2,3,4,5,6 |
| 22 | 6 | 1,2,3,4,5,7 |
| 38 | 6 | 3,5,6,7,8,9 |
| 39 | 6 | 4,5,6,7,8,9 |
| 28 | 7 | 1,2,3,4,5,6,7 |
| 29 | 7 | 1,2,3,4,5,6,8 |
| 41 | 7 | 2,4,5,6,7,8,9 |
| 42 | 7 | 3,4,5,6,7,8,9 |
| Any | 8 | 1-9 except 45 minus clue value |
| Any | 9 | 1-9 inclusive |
The absolutely exhaustive combination of all cage clues, cage sizes
and the combination of combinations for those cage size/values is:
and the combination of combinations for those cage size/values is:
| Cage Size | Cage Value | Combination | Combos Combined |
| 2 | 3 | 1/2 | Unique |
| 2 | 4 | 1/3 | Unique |
| 2 | 5 | 1/4 | |
| 2 | 5 | 2/3 | 1/2/3/4 |
| 2 | 6 | 1/5 | |
| 2 | 6 | 2/4 | 1/2/4/5 |
| 2 | 7 | 1/6 | |
| 2 | 7 | 2/5 | |
| 2 | 7 | 3/4 | 1/2/3/4/5/6 |
| 2 | 8 | 1/7 | |
| 2 | 8 | 2/6 | |
| 2 | 8 | 3/5 | 1/2/3/5/6/7 |
| 2 | 9 | 1/8 | |
| 2 | 9 | 2/7 | |
| 2 | 9 | 3/6 | |
| 2 | 9 | 4/5 | 1/2/3/4/5/6/7/8 |
| 2 | 10 | 1/9 | |
| 2 | 10 | 2/8 | |
| 2 | 10 | 3/7 | |
| 2 | 10 | 4/6 | 1/2/3/4/6/7/8/9 |
| 2 | 11 | 2/9 | |
| 2 | 11 | 3/8 | |
| 2 | 11 | 4/7 | |
| 2 | 11 | 5/6 | 2/3/4/5/6/7/8/9 |
| 2 | 12 | 3/9 | |
| 2 | 12 | 4/8 | |
| 2 | 12 | 5/7 | 3/4/5/7/8/9 |
| 2 | 13 | 4/9 | |
| 2 | 13 | 5/8 | |
| 2 | 13 | 6/7 | 4/5/6/7/8/9 |
| 2 | 14 | 5/9 | |
| 2 | 14 | 6/8 | 5/6/8/9 |
| 2 | 15 | 6/9 | |
| 2 | 15 | 7/8 | 6/7/8/9 |
| 2 | 16 | 7/9 | Unique |
| 2 | 17 | 8/9 | Unique |
| 3 | 6 | 1/2/3 | Unique |
| 3 | 7 | 1/2/4 | Unique |
| 3 | 8 | 1/2/5 | |
| 3 | 8 | 1/3/4 | 1/2/3/4/5 |
| 3 | 9 | 1/2/6 | |
| 3 | 9 | 1/3/5 | |
| 3 | 9 | 2/3/4 | 1/2/3/4/5/6 |
| 3 | 10 | 1/2/7 | |
| 3 | 10 | 1/3/6 | |
| 3 | 10 | 1/4/5 | |
| 3 | 10 | 2/3/5 | 1/2/3/4/5/6/7 |
| 3 | 11 | 1/2/8 | |
| 3 | 11 | 1/3/7 | |
| 3 | 11 | 1/4/6 | |
| 3 | 11 | 2/3/6 | |
| 3 | 11 | 2/4/5 | 1/2/3/4/5/6/7/8 |
| 3 | 12 | 1/2/9 | |
| 3 | 12 | 1/3/8 | |
| 3 | 12 | 1/4/7 | |
| 3 | 12 | 1/5/6 | |
| 3 | 12 | 2/3/7 | |
| 3 | 12 | 2/4/6 | |
| 3 | 12 | 3/4/5 | 1/2/3/4/5/6/7/8/9 |
| 3 | 13 | 1/3/9 | |
| 3 | 13 | 1/4/8 | |
| 3 | 13 | 1/5/7 | |
| 3 | 13 | 2/3/8 | |
| 3 | 13 | 2/4/7 | |
| 3 | 13 | 2/5/6 | |
| 3 | 13 | 3/4/6 | 1/2/3/4/5/6/7/8/9 |
| 3 | 14 | 1/4/9 | |
| 3 | 14 | 1/5/8 | |
| 3 | 14 | 1/6/7 | |
| 3 | 14 | 2/3/9 | |
| 3 | 14 | 2/4/8 | |
| 3 | 14 | 2/5/7 | |
| 3 | 14 | 3/4/7 | |
| 3 | 14 | 3/5/6 | 1/2/3/4/5/6/7/8/9 |
| 3 | 15 | 1/5/9 | |
| 3 | 15 | 1/6/8 | |
| 3 | 15 | 2/4/9 | |
| 3 | 15 | 2/5/8 | |
| 3 | 15 | 2/6/7 | |
| 3 | 15 | 3/4/8 | |
| 3 | 15 | 3/5/7 | |
| 3 | 15 | 4/5/6 | 1/2/3/4/5/6/7/8/9 |
| 3 | 16 | 1/6/9 | |
| 3 | 16 | 1/7/8 | |
| 3 | 16 | 2/5/9 | |
| 3 | 16 | 2/6/8 | |
| 3 | 16 | 3/4/9 | |
| 3 | 16 | 3/5/8 | |
| 3 | 16 | 3/6/7 | |
| 3 | 16 | 4/5/7 | 1/2/3/4/5/6/7/8/9 |
| 3 | 17 | 1/7/9 | |
| 3 | 17 | 2/6/9 | |
| 3 | 17 | 2/7/8 | |
| 3 | 17 | 3/5/9 | |
| 3 | 17 | 3/6/8 | |
| 3 | 17 | 4/5/8 | |
| 3 | 17 | 4/6/7 | 1/2/3/4/5/6/7/8/9 |
| 3 | 18 | 1/8/9 | |
| 3 | 18 | 2/7/9 | |
| 3 | 18 | 3/6/9 | |
| 3 | 18 | 3/7/8 | |
| 3 | 18 | 4/5/9 | |
| 3 | 18 | 4/6/8 | |
| 3 | 18 | 5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 3 | 19 | 2/8/9 | |
| 3 | 19 | 3/7/9 | |
| 3 | 19 | 4/6/9 | |
| 3 | 19 | 4/7/8 | |
| 3 | 19 | 5/6/8 | 2/3/4/5/6/7/8/9 |
| 3 | 20 | 3/8/9 | |
| 3 | 20 | 4/7/9 | |
| 3 | 20 | 5/6/9 | |
| 3 | 20 | 5/7/8 | 3/4/5/6/7/8/9 |
| 3 | 21 | 4/8/9 | |
| 3 | 21 | 5/7/9 | |
| 3 | 21 | 6/7/8 | 4/5/6/7/8/9 |
| 3 | 22 | 5/8/9 | |
| 3 | 22 | 6/7/9 | 5/6/7/8/9 |
| 3 | 23 | 6/8/9 | Unique |
| 3 | 24 | 7/8/9 | Unique |
| 4 | 10 | 1/2/3/4 | Unique |
| 4 | 11 | 1/2/3/5 | Unique |
| 4 | 12 | 1/2/3/6 | |
| 4 | 12 | 1/2/4/5 | 1/2/3/4/5/6 |
| 4 | 13 | 1/2/3/7 | |
| 4 | 13 | 1/2/4/6 | |
| 4 | 13 | 1/3/4/5 | 1/2/3/4/5/6/7 |
| 4 | 14 | 1/2/3/8 | |
| 4 | 14 | 1/2/4/7 | |
| 4 | 14 | 1/2/5/6 | |
| 4 | 14 | 1/3/4/6 | |
| 4 | 14 | 2/3/4/5 | 1/2/3/4/5/6/7/8 |
| 4 | 15 | 1/2/3/9 | |
| 4 | 15 | 1/2/4/8 | |
| 4 | 15 | 1/2/5/7 | |
| 4 | 15 | 1/3/4/7 | |
| 4 | 15 | 1/3/5/6 | |
| 4 | 15 | 2/3/4/6 | 1/2/3/4/5/6/7/8/9 |
| 4 | 16 | 1/2/4/9 | |
| 4 | 16 | 1/2/5/8 | |
| 4 | 16 | 1/2/6/7 | |
| 4 | 16 | 1/3/4/8 | |
| 4 | 16 | 1/3/5/7 | |
| 4 | 16 | 1/4/5/6 | |
| 4 | 16 | 2/3/4/7 | |
| 4 | 16 | 2/3/5/6 | 1/2/3/4/5/6/7/8/9 |
| 4 | 17 | 1/2/5/9 | |
| 4 | 17 | 1/2/6/8 | |
| 4 | 17 | 1/3/4/9 | |
| 4 | 17 | 1/3/5/8 | |
| 4 | 17 | 1/3/6/7 | |
| 4 | 17 | 1/4/5/7 | |
| 4 | 17 | 2/3/4/8 | |
| 4 | 17 | 2/3/5/7 | |
| 4 | 17 | 2/4/5/6 | 1/2/3/4/5/6/7/8/9 |
| 4 | 18 | 1/2/6/9 | |
| 4 | 18 | 1/2/7/8 | |
| 4 | 18 | 1/3/5/9 | |
| 4 | 18 | 1/3/6/8 | |
| 4 | 18 | 1/4/5/8 | |
| 4 | 18 | 1/4/6/7 | |
| 4 | 18 | 2/3/4/9 | |
| 4 | 18 | 2/3/5/8 | |
| 4 | 18 | 2/3/6/7 | |
| 4 | 18 | 2/4/5/7 | |
| 4 | 18 | 3/4/5/6 | 1/2/3/4/5/6/7/8/9 |
| 4 | 19 | 1/2/7/9 | |
| 4 | 19 | 1/3/6/9 | |
| 4 | 19 | 1/3/7/8 | |
| 4 | 19 | 1/4/5/9 | |
| 4 | 19 | 1/4/6/8 | |
| 4 | 19 | 1/5/6/7 | |
| 4 | 19 | 2/3/5/9 | |
| 4 | 19 | 2/3/6/8 | |
| 4 | 19 | 2/4/5/8 | |
| 4 | 19 | 2/4/6/7 | |
| 4 | 19 | 3/4/5/7 | 1/2/3/4/5/6/7/8/9 |
| 4 | 20 | 1/2/8/9 | |
| 4 | 20 | 1/3/7/9 | |
| 4 | 20 | 1/4/6/9 | |
| 4 | 20 | 1/4/7/8 | |
| 4 | 20 | 1/5/6/8 | |
| 4 | 20 | 2/3/6/9 | |
| 4 | 20 | 2/3/7/8 | |
| 4 | 20 | 2/4/5/9 | |
| 4 | 20 | 2/4/6/8 | |
| 4 | 20 | 2/5/6/7 | |
| 4 | 20 | 3/4/5/8 | |
| 4 | 20 | 3/4/6/7 | 1/2/3/4/5/6/7/8/9 |
| 4 | 21 | 1/3/8/9 | |
| 4 | 21 | 1/4/7/9 | |
| 4 | 21 | 1/5/6/9 | |
| 4 | 21 | 1/5/7/8 | |
| 4 | 21 | 2/3/7/9 | |
| 4 | 21 | 2/4/6/9 | |
| 4 | 21 | 2/4/7/8 | |
| 4 | 21 | 2/5/6/8 | |
| 4 | 21 | 3/4/5/9 | |
| 4 | 21 | 3/4/6/8 | |
| 4 | 21 | 3/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 4 | 22 | 1/4/8/9 | |
| 4 | 22 | 1/5/7/9 | |
| 4 | 22 | 1/6/7/8 | |
| 4 | 22 | 2/3/8/9 | |
| 4 | 22 | 2/4/7/9 | |
| 4 | 22 | 2/5/6/9 | |
| 4 | 22 | 2/5/7/8 | |
| 4 | 22 | 3/4/6/9 | |
| 4 | 22 | 3/4/7/8 | |
| 4 | 22 | 3/5/6/8 | |
| 4 | 22 | 4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 4 | 23 | 1/5/8/9 | |
| 4 | 23 | 1/6/7/9 | |
| 4 | 23 | 2/4/8/9 | |
| 4 | 23 | 2/5/7/9 | |
| 4 | 23 | 2/6/7/8 | |
| 4 | 23 | 3/4/7/9 | |
| 4 | 23 | 3/5/6/9 | |
| 4 | 23 | 3/5/7/8 | |
| 4 | 23 | 4/5/6/8 | 1/2/3/4/5/6/7/8/9 |
| 4 | 24 | 1/6/8/9 | |
| 4 | 24 | 2/5/8/9 | |
| 4 | 24 | 2/6/7/9 | |
| 4 | 24 | 3/4/8/9 | |
| 4 | 24 | 3/5/7/9 | |
| 4 | 24 | 3/6/7/8 | |
| 4 | 24 | 4/5/6/9 | |
| 4 | 24 | 4/5/7/8 | 1/2/3/4/5/6/7/8/9 |
| 4 | 25 | 1/7/8/9 | |
| 4 | 25 | 2/6/8/9 | |
| 4 | 25 | 3/5/8/9 | |
| 4 | 25 | 3/6/7/9 | |
| 4 | 25 | 4/5/7/9 | |
| 4 | 25 | 4/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 4 | 26 | 2/7/8/9 | |
| 4 | 26 | 3/6/8/9 | |
| 4 | 26 | 4/5/8/9 | |
| 4 | 26 | 4/6/7/9 | |
| 4 | 26 | 5/6/7/8 | 2/3/4/5/6/7/8/9 |
| 4 | 27 | 3/7/8/9 | |
| 4 | 27 | 4/6/8/9 | |
| 4 | 27 | 5/6/7/9 | 3/4/5/6/7/8/9 |
| 4 | 28 | 4/7/8/9 | |
| 4 | 28 | 5/6/8/9 | 4/5/6/7/8/9 |
| 4 | 29 | 5/7/8/9 | Unique |
| 4 | 30 | 6/7/8/9 | Unique |
| 5 | 15 | 1/2/3/4/5 | Unique |
| 5 | 16 | 1/2/3/4/6 | Unique |
| 5 | 17 | 1/2/3/4/7 | |
| 5 | 17 | 1/2/3/5/6 | 1/2/3/4/5/6/7 |
| 5 | 18 | 1/2/3/4/8 | |
| 5 | 18 | 1/2/3/5/7 | |
| 5 | 18 | 1/2/4/5/6 | 1/2/3/4/5/6/7/8 |
| 5 | 19 | 1/2/3/4/9 | |
| 5 | 19 | 1/2/3/5/8 | |
| 5 | 19 | 1/2/3/6/7 | |
| 5 | 19 | 1/2/4/5/7 | |
| 5 | 19 | 1/3/4/5/6 | 1/2/3/4/5/6/7/8/9 |
| 5 | 20 | 1/2/3/5/9 | |
| 5 | 20 | 1/2/3/6/8 | |
| 5 | 20 | 1/2/4/5/8 | |
| 5 | 20 | 1/2/4/6/7 | |
| 5 | 20 | 1/3/4/5/7 | |
| 5 | 20 | 2/3/4/5/6 | 1/2/3/4/5/6/7/8/9 |
| 5 | 21 | 1/2/3/6/9 | |
| 5 | 21 | 1/2/3/7/8 | |
| 5 | 21 | 1/2/4/5/9 | |
| 5 | 21 | 1/2/4/6/8 | |
| 5 | 21 | 1/2/5/6/7 | |
| 5 | 21 | 1/3/4/5/8 | |
| 5 | 21 | 1/3/4/6/7 | |
| 5 | 21 | 2/3/4/5/7 | 1/2/3/4/5/6/7/8/9 |
| 5 | 22 | 1/2/3/7/9 | |
| 5 | 22 | 1/2/4/6/9 | |
| 5 | 22 | 1/2/4/7/8 | |
| 5 | 22 | 1/2/5/6/8 | |
| 5 | 22 | 1/3/4/5/9 | |
| 5 | 22 | 1/3/4/6/8 | |
| 5 | 22 | 1/3/5/6/7 | |
| 5 | 22 | 2/3/4/5/8 | |
| 5 | 22 | 2/3/4/6/7 | 1/2/3/4/5/6/7/8/9 |
| 5 | 23 | 1/2/3/8/9 | |
| 5 | 23 | 1/2/4/7/9 | |
| 5 | 23 | 1/2/5/6/9 | |
| 5 | 23 | 1/2/5/7/8 | |
| 5 | 23 | 1/3/4/6/9 | |
| 5 | 23 | 1/3/4/7/8 | |
| 5 | 23 | 1/3/5/6/8 | |
| 5 | 23 | 1/4/5/6/7 | |
| 5 | 23 | 2/3/4/5/9 | |
| 5 | 23 | 2/3/4/6/8 | |
| 5 | 23 | 2/3/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 5 | 24 | 1/2/4/8/9 | |
| 5 | 24 | 1/2/5/7/9 | |
| 5 | 24 | 1/2/6/7/8 | |
| 5 | 24 | 1/3/4/7/9 | |
| 5 | 24 | 1/3/5/6/9 | |
| 5 | 24 | 1/3/5/7/8 | |
| 5 | 24 | 1/4/5/6/8 | |
| 5 | 24 | 2/3/4/6/9 | |
| 5 | 24 | 2/3/4/7/8 | |
| 5 | 24 | 2/3/5/6/8 | |
| 5 | 24 | 2/4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 5 | 25 | 1/2/5/8/9 | |
| 5 | 25 | 1/2/6/7/9 | |
| 5 | 25 | 1/3/4/8/9 | |
| 5 | 25 | 1/3/5/7/9 | |
| 5 | 25 | 1/3/6/7/8 | |
| 5 | 25 | 1/4/5/6/9 | |
| 5 | 25 | 1/4/5/7/8 | |
| 5 | 25 | 2/3/4/7/9 | |
| 5 | 25 | 2/3/5/6/9 | |
| 5 | 25 | 2/3/5/7/8 | |
| 5 | 25 | 2/4/5/6/8 | |
| 5 | 25 | 3/4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 5 | 26 | 1/2/6/8/9 | |
| 5 | 26 | 1/3/5/8/9 | |
| 5 | 26 | 1/3/6/7/9 | |
| 5 | 26 | 1/4/5/7/9 | |
| 5 | 26 | 1/4/6/7/8 | |
| 5 | 26 | 2/3/4/8/9 | |
| 5 | 26 | 2/3/5/7/9 | |
| 5 | 26 | 2/3/6/7/8 | |
| 5 | 26 | 2/4/5/6/9 | |
| 5 | 26 | 2/4/5/7/8 | |
| 5 | 26 | 3/4/5/6/8 | 1/2/3/4/5/6/7/8/9 |
| 5 | 27 | 1/2/7/8/9 | |
| 5 | 27 | 1/3/6/8/9 | |
| 5 | 27 | 1/4/5/8/9 | |
| 5 | 27 | 1/4/6/7/9 | |
| 5 | 27 | 1/5/6/7/8 | |
| 5 | 27 | 2/3/5/8/9 | |
| 5 | 27 | 2/3/6/7/9 | |
| 5 | 27 | 2/4/5/7/9 | |
| 5 | 27 | 2/4/6/7/8 | |
| 5 | 27 | 3/4/5/6/9 | |
| 5 | 27 | 3/4/5/7/8 | 1/2/3/4/5/6/7/8/9 |
| 5 | 28 | 1/3/7/8/9 | |
| 5 | 28 | 1/4/6/8/9 | |
| 5 | 28 | 1/5/6/7/9 | |
| 5 | 28 | 2/3/6/8/9 | |
| 5 | 28 | 2/4/5/8/9 | |
| 5 | 28 | 2/4/6/7/9 | |
| 5 | 28 | 2/5/6/7/8 | |
| 5 | 28 | 3/4/5/7/9 | |
| 5 | 28 | 3/4/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 5 | 29 | 1/4/7/8/9 | |
| 5 | 29 | 1/5/6/8/9 | |
| 5 | 29 | 2/3/7/8/9 | |
| 5 | 29 | 2/4/6/8/9 | |
| 5 | 29 | 2/5/6/7/9 | |
| 5 | 29 | 3/4/5/8/9 | |
| 5 | 29 | 3/4/6/7/9 | |
| 5 | 29 | 3/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 5 | 30 | 1/5/7/8/9 | |
| 5 | 30 | 2/4/7/8/9 | |
| 5 | 30 | 2/5/6/8/9 | |
| 5 | 30 | 3/4/6/8/9 | |
| 5 | 30 | 3/5/6/7/9 | |
| 5 | 30 | 4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 5 | 31 | 1/6/7/8/9 | |
| 5 | 31 | 2/5/7/8/9 | |
| 5 | 31 | 3/4/7/8/9 | |
| 5 | 31 | 3/5/6/8/9 | |
| 5 | 31 | 4/5/6/7/9 | 1/2/3/4/5/6/7/8/9 |
| 5 | 32 | 2/6/7/8/9 | |
| 5 | 32 | 3/5/7/8/9 | |
| 5 | 32 | 4/5/6/8/9 | 2/3/4/5/6/7/8/9 |
| 5 | 33 | 3/6/7/8/9 | |
| 5 | 33 | 4/5/7/8/9 | 3/4/5/6/7/8/9 |
| 5 | 34 | 4/6/7/8/9 | Unique |
| 5 | 35 | 5/6/7/8/9 | Unique |
| 6 | 21 | 1/2/3/4/5/6 | Unique |
| 6 | 22 | 1/2/3/4/5/7 | Unique |
| 6 | 23 | 1/2/3/4/5/8 | |
| 6 | 23 | 1/2/3/4/6/7 | 1/2/3/4/5/6/7/8 |
| 6 | 24 | 1/2/3/4/5/9 | |
| 6 | 24 | 1/2/3/4/6/8 | |
| 6 | 24 | 1/2/3/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 6 | 25 | 1/2/3/4/6/9 | |
| 6 | 25 | 1/2/3/4/7/8 | |
| 6 | 25 | 1/2/3/5/6/8 | |
| 6 | 25 | 1/2/4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 6 | 26 | 1/2/3/4/7/9 | |
| 6 | 26 | 1/2/3/5/6/9 | |
| 6 | 26 | 1/2/3/5/7/8 | |
| 6 | 26 | 1/2/4/5/6/8 | |
| 6 | 26 | 1/3/4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 6 | 27 | 1/2/3/4/8/9 | |
| 6 | 27 | 1/2/3/5/7/9 | |
| 6 | 27 | 1/2/3/6/7/8 | |
| 6 | 27 | 1/2/4/5/6/9 | |
| 6 | 27 | 1/2/4/5/7/8 | |
| 6 | 27 | 1/3/4/5/6/8 | |
| 6 | 27 | 2/3/4/5/6/7 | 1/2/3/4/5/6/7/8/9 |
| 6 | 28 | 1/2/3/5/8/9 | |
| 6 | 28 | 1/2/3/6/7/9 | |
| 6 | 28 | 1/2/4/5/7/9 | |
| 6 | 28 | 1/2/4/6/7/8 | |
| 6 | 28 | 1/3/4/5/6/9 | |
| 6 | 28 | 1/3/4/5/7/8 | |
| 6 | 28 | 2/3/4/5/6/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 29 | 1/2/3/6/8/9 | |
| 6 | 29 | 1/2/4/5/8/9 | |
| 6 | 29 | 1/2/4/6/7/9 | |
| 6 | 29 | 1/2/5/6/7/8 | |
| 6 | 29 | 1/3/4/5/7/9 | |
| 6 | 29 | 1/3/4/6/7/8 | |
| 6 | 29 | 2/3/4/5/6/9 | |
| 6 | 29 | 2/3/4/5/7/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 30 | 1/2/3/7/8/9 | |
| 6 | 30 | 1/2/4/6/8/9 | |
| 6 | 30 | 1/2/5/6/7/9 | |
| 6 | 30 | 1/3/4/5/8/9 | |
| 6 | 30 | 1/3/4/6/7/9 | |
| 6 | 30 | 1/3/5/6/7/8 | |
| 6 | 30 | 2/3/4/5/7/9 | |
| 6 | 30 | 2/3/4/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 31 | 1/2/4/7/8/9 | |
| 6 | 31 | 1/2/5/6/8/9 | |
| 6 | 31 | 1/3/4/6/8/9 | |
| 6 | 31 | 1/3/5/6/7/9 | |
| 6 | 31 | 1/4/5/6/7/8 | |
| 6 | 31 | 2/3/4/5/8/9 | |
| 6 | 31 | 2/3/4/6/7/9 | |
| 6 | 31 | 2/3/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 32 | 1/2/5/7/8/9 | |
| 6 | 32 | 1/3/4/7/8/9 | |
| 6 | 32 | 1/3/5/6/8/9 | |
| 6 | 32 | 1/4/5/6/7/9 | |
| 6 | 32 | 2/3/4/6/8/9 | |
| 6 | 32 | 2/3/5/6/7/9 | |
| 6 | 32 | 2/4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 33 | 1/2/6/7/8/9 | |
| 6 | 33 | 1/3/5/7/8/9 | |
| 6 | 33 | 1/4/5/6/8/9 | |
| 6 | 33 | 2/3/4/7/8/9 | |
| 6 | 33 | 2/3/5/6/8/9 | |
| 6 | 33 | 2/4/5/6/7/9 | |
| 6 | 33 | 3/4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 6 | 34 | 1/3/6/7/8/9 | |
| 6 | 34 | 1/4/5/7/8/9 | |
| 6 | 34 | 2/3/5/7/8/9 | |
| 6 | 34 | 2/4/5/6/8/9 | |
| 6 | 34 | 3/4/5/6/7/9 | 1/2/3/4/5/6/7/8/9 |
| 6 | 35 | 1/4/6/7/8/9 | |
| 6 | 35 | 2/3/6/7/8/9 | |
| 6 | 35 | 2/4/5/7/8/9 | |
| 6 | 35 | 3/4/5/6/8/9 | 1/2/3/4/5/6/7/8/9 |
| 6 | 36 | 1/5/6/7/8/9 | |
| 6 | 36 | 2/4/6/7/8/9 | |
| 6 | 36 | 3/4/5/7/8/9 | 1/2/3/4/5/6/7/8/9 |
| 6 | 37 | 2/5/6/7/8/9 | |
| 6 | 37 | 3/4/6/7/8/9 | 2/3/4/5/6/7/8/9 |
| 6 | 38 | 3/5/6/7/8/9 | Unique |
| 6 | 39 | 4/5/6/7/8/9 | Unique |
| 7 | 28 | 1/2/3/4/5/6/7 | Unique |
| 7 | 29 | 1/2/3/4/5/6/8 | Unique |
| 7 | 30 | 1/2/3/4/5/6/9 | |
| 7 | 30 | 1/2/3/4/5/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 31 | 1/2/3/4/5/7/9 | |
| 7 | 31 | 1/2/3/4/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 32 | 1/2/3/4/5/8/9 | |
| 7 | 32 | 1/2/3/4/6/7/9 | |
| 7 | 32 | 1/2/3/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 33 | 1/2/3/4/6/8/9 | |
| 7 | 33 | 1/2/3/5/6/7/9 | |
| 7 | 33 | 1/2/4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 34 | 1/2/3/4/7/8/9 | |
| 7 | 34 | 1/2/3/5/6/8/9 | |
| 7 | 34 | 1/2/4/5/6/7/9 | |
| 7 | 34 | 1/3/4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 35 | 1/2/3/5/7/8/9 | |
| 7 | 35 | 1/2/4/5/6/8/9 | |
| 7 | 35 | 1/3/4/5/6/7/9 | |
| 7 | 35 | 2/3/4/5/6/7/8 | 1/2/3/4/5/6/7/8/9 |
| 7 | 36 | 1/2/3/6/7/8/9 | |
| 7 | 36 | 1/2/4/5/7/8/9 | |
| 7 | 36 | 1/3/4/5/6/8/9 | |
| 7 | 36 | 2/3/4/5/6/7/9 | 1/2/3/4/5/6/7/8/9 |
| 7 | 37 | 1/2/4/6/7/8/9 | |
| 7 | 37 | 1/3/4/5/7/8/9 | |
| 7 | 37 | 2/3/4/5/6/8/9 | 1/2/3/4/5/6/7/8/9 |
| 7 | 38 | 1/2/5/6/7/8/9 | |
| 7 | 38 | 1/3/4/6/7/8/9 | |
| 7 | 38 | 2/3/4/5/7/8/9 | 1/2/3/4/5/6/7/8/9 |
| 7 | 39 | 1/3/5/6/7/8/9 | |
| 7 | 39 | 2/3/4/6/7/8/9 | 1/2/3/4/5/6/7/8/9 |
| 7 | 40 | 1/4/5/6/7/8/9 | |
| 7 | 40 | 2/3/5/6/7/8/9 | 1/2/3/4/5/6/7/8/9 |
| 7 | 41 | 2/4/5/6/7/8/9 | Unique |
| 7 | 42 | 3/4/5/6/7/8/9 | Unique |
| 8 | 36 | 1/2/3/4/5/6/7/8 | Unique |
| 8 | 37 | 1/2/3/4/5/6/7/9 | Unique |
| 8 | 38 | 1/2/3/4/5/6/8/9 | Unique |
| 8 | 39 | 1/2/3/4/5/7/8/9 | Unique |
| 8 | 40 | 1/2/3/4/6/7/8/9 | Unique |
| 8 | 41 | 1/2/3/5/6/7/8/9 | Unique |
| 8 | 42 | 1/2/4/5/6/7/8/9 | Unique |
| 8 | 43 | 1/3/4/5/6/7/8/9 | Unique |
| 8 | 44 | 2/3/4/5/6/7/8/9 | Unique |
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