Killer sudoku combinations

This table shows every set of different digits from 1 to 9 for each cage size and sum. A combination like 1269 means the cage holds 1, 2, 6 and 9 in some order. Highlighted rows have only one combination, which makes them the best place to start.

Tip: in the game, select a square and the combinations for its cage are shown under the grid. Play today’s killer sudoku.

Cages of 2 cells (sums 3 to 17)

Cages of 3 cells (sums 6 to 24)

Cages of 4 cells (sums 10 to 30)

Cages of 5 cells (sums 15 to 35)

Cages of 6 cells (sums 21 to 39)

Cages of 7 cells (sums 28 to 42)

Cages of 8 cells (sums 36 to 44)

Cages of 9 cells (sums 45 to 45)

Questions

How many killer sudoku combinations are there?

For cages of 2 to 9 cells there are 502 combinations of different digits from 1 to 9. The table lists every one of them.

Which cage sums have only one combination?

In two cells: 3 = 1+2, 4 = 1+3, 16 = 7+9, 17 = 8+9. In three cells: 6 = 1+2+3, 7 = 1+2+4, 23 = 6+8+9, 24 = 7+8+9. In four cells: 10 = 1+2+3+4, 11 = 1+2+3+5, 29 = 5+7+8+9, 30 = 6+7+8+9. They are highlighted in the table.

Can a digit repeat in a cage?

No. In killer sudoku the digits inside one cage are always different, so every combination in the table uses different digits.

For cages of one cell, the sum is the digit itself.