How to use the combinations chart
Find the table for the number of cells in your cage, then the row for its sum. The digits listed are every set of different digits that adds up to that sum. For example, a 3-cell cage of 10 can be 1 2 7, 1 3 6, 1 4 5 or 2 3 5. No combination ever repeats a digit, because a digit cannot appear twice in the same cage.
The calculator does the same lookup and lets you filter. Mark a digit under Must include when you have already placed it in the cage or know it belongs there, and under Rule out when the cage's row, column or box already has it. The result shows what is left, which digits every remaining combination uses, and which digits none of them use.
Combinations worth knowing by heart
For cages of 2 to 7 cells, the two smallest and the two largest sums can each be made only one way. These cages are the usual starting points of a puzzle:
- 2 cells: 3 = 12, 4 = 13, 16 = 79, 17 = 89
- 3 cells: 6 = 123, 7 = 124, 23 = 689, 24 = 789
- 4 cells: 10 = 1234, 11 = 1235, 29 = 5789, 30 = 6789
- 5 cells: 15 = 12345, 16 = 12346, 34 = 46789, 35 = 56789
A cage in the middle of its range is the opposite: a 4-cell cage of 20 or a 5-cell cage of 25 can be filled in 12 different ways, so start elsewhere and come back to it.
Big cages: think about the missing digits
A cage of 6 or more cells is easier to read by what it leaves out. Nine digits add up to 45, so a 7-cell cage of 38 is missing two digits that add up to 7: 1 and 6, 2 and 5, or 3 and 4. An 8-cell cage always misses exactly one digit, 45 minus its sum, and a 9-cell cage holds every digit once. That is why the tables for 6 to 9 cells are short.
How many combinations are there?
For cages of 2 to 9 cells there are 502 combinations in all: 36 for 2 cells, 84 for 3, 126 each for 4 and 5, 84 for 6, 36 for 7, 9 for 8 and 1 for 9. The counts are symmetric because choosing the digits in a cage is the same as choosing the digits left out of it.
Printing the cheat sheet
Use Print cheat sheet above the chart, or your browser's print command. The printout leaves out the calculator and this text and fits all eight tables on one page, with the one-combination sums shaded. Choose "Save as PDF" in the print dialog if you want a file instead of paper.
Ready to use it? Play Killer Sudoku online, or try a classic Sudoku first if you are new to the rules.
Frequently asked questions
How many Killer Sudoku combinations are there?
502 for cages of 2 to 9 cells: 36, 84, 126, 126, 84, 36, 9 and 1 for 2, 3, 4, 5, 6, 7, 8 and 9 cells.
What are the smallest and largest sums for each cage size?
2 cells: 3 to 17. 3 cells: 6 to 24. 4 cells: 10 to 30. 5 cells: 15 to 35. 6 cells: 21 to 39. 7 cells: 28 to 42. 8 cells: 36 to 44. 9 cells: always 45.
Which cage sums have only one combination?
For 2 to 7 cells, the two lowest and the two highest sums: for example 3 and 4 or 16 and 17 in two cells, and 6 and 7 or 23 and 24 in three cells. Every 8-cell sum has one combination too, because the cage misses exactly one digit.
Can a digit appear twice in a cage?
No. In Killer Sudoku the digits inside a cage are all different, so the chart and the calculator only list sets of distinct digits.
Can I print this Killer Sudoku cheat sheet?
Yes. The Print cheat sheet button prints only the chart, on a single page. Pick "Save as PDF" in the print dialog to keep it as a file.