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 Killer Combinations From sudokuwiki.org, the puzzle solver's site
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.

 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 45minus 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:

 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 Unique 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

 Article created on 12-April-2008. Views: 24270This page was last modified on 18-May-2013, at 06:06.All text is copyright and for personal use only but may be reproduced with the permission of the author. Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2013