Killer Sudoku Combinations Calculator
Enter a cage sum and how many cells it covers to see every valid combination of digits. Narrow the list with digits you already know are in or out of the cage, then use the full reference below as a printable cheat sheet.
Unique combinations (forced cages)
These 34 cages have exactly one possible set of digits — the moment you see the sum and size, the digits are fixed. Worth memorising.
Full combinations reference
Every cage sum and its combinations, grouped by cage size (502 in total). Rows with a single combination are highlighted — those are the forced cages above. Tap a size to expand.
2-cell cages sums 3–17
| Sum | Combinations |
|---|---|
| 3 | 1 2 |
| 4 | 1 3 |
| 5 | 1 42 3 |
| 6 | 1 52 4 |
| 7 | 1 62 53 4 |
| 8 | 1 72 63 5 |
| 9 | 1 82 73 64 5 |
| 10 | 1 92 83 74 6 |
| 11 | 2 93 84 75 6 |
| 12 | 3 94 85 7 |
| 13 | 4 95 86 7 |
| 14 | 5 96 8 |
| 15 | 6 97 8 |
| 16 | 7 9 |
| 17 | 8 9 |
3-cell cages sums 6–24
| Sum | Combinations |
|---|---|
| 6 | 1 2 3 |
| 7 | 1 2 4 |
| 8 | 1 2 51 3 4 |
| 9 | 1 2 61 3 52 3 4 |
| 10 | 1 2 71 3 61 4 52 3 5 |
| 11 | 1 2 81 3 71 4 62 3 62 4 5 |
| 12 | 1 2 91 3 81 4 71 5 62 3 72 4 63 4 5 |
| 13 | 1 3 91 4 81 5 72 3 82 4 72 5 63 4 6 |
| 14 | 1 4 91 5 81 6 72 3 92 4 82 5 73 4 73 5 6 |
| 15 | 1 5 91 6 82 4 92 5 82 6 73 4 83 5 74 5 6 |
| 16 | 1 6 91 7 82 5 92 6 83 4 93 5 83 6 74 5 7 |
| 17 | 1 7 92 6 92 7 83 5 93 6 84 5 84 6 7 |
| 18 | 1 8 92 7 93 6 93 7 84 5 94 6 85 6 7 |
| 19 | 2 8 93 7 94 6 94 7 85 6 8 |
| 20 | 3 8 94 7 95 6 95 7 8 |
| 21 | 4 8 95 7 96 7 8 |
| 22 | 5 8 96 7 9 |
| 23 | 6 8 9 |
| 24 | 7 8 9 |
4-cell cages sums 10–30
| Sum | Combinations |
|---|---|
| 10 | 1 2 3 4 |
| 11 | 1 2 3 5 |
| 12 | 1 2 3 61 2 4 5 |
| 13 | 1 2 3 71 2 4 61 3 4 5 |
| 14 | 1 2 3 81 2 4 71 2 5 61 3 4 62 3 4 5 |
| 15 | 1 2 3 91 2 4 81 2 5 71 3 4 71 3 5 62 3 4 6 |
| 16 | 1 2 4 91 2 5 81 2 6 71 3 4 81 3 5 71 4 5 62 3 4 72 3 5 6 |
| 17 | 1 2 5 91 2 6 81 3 4 91 3 5 81 3 6 71 4 5 72 3 4 82 3 5 72 4 5 6 |
| 18 | 1 2 6 91 2 7 81 3 5 91 3 6 81 4 5 81 4 6 72 3 4 92 3 5 82 3 6 72 4 5 73 4 5 6 |
| 19 | 1 2 7 91 3 6 91 3 7 81 4 5 91 4 6 81 5 6 72 3 5 92 3 6 82 4 5 82 4 6 73 4 5 7 |
| 20 | 1 2 8 91 3 7 91 4 6 91 4 7 81 5 6 82 3 6 92 3 7 82 4 5 92 4 6 82 5 6 73 4 5 83 4 6 7 |
| 21 | 1 3 8 91 4 7 91 5 6 91 5 7 82 3 7 92 4 6 92 4 7 82 5 6 83 4 5 93 4 6 83 5 6 7 |
| 22 | 1 4 8 91 5 7 91 6 7 82 3 8 92 4 7 92 5 6 92 5 7 83 4 6 93 4 7 83 5 6 84 5 6 7 |
| 23 | 1 5 8 91 6 7 92 4 8 92 5 7 92 6 7 83 4 7 93 5 6 93 5 7 84 5 6 8 |
| 24 | 1 6 8 92 5 8 92 6 7 93 4 8 93 5 7 93 6 7 84 5 6 94 5 7 8 |
| 25 | 1 7 8 92 6 8 93 5 8 93 6 7 94 5 7 94 6 7 8 |
| 26 | 2 7 8 93 6 8 94 5 8 94 6 7 95 6 7 8 |
| 27 | 3 7 8 94 6 8 95 6 7 9 |
| 28 | 4 7 8 95 6 8 9 |
| 29 | 5 7 8 9 |
| 30 | 6 7 8 9 |
5-cell cages sums 15–35
| Sum | Combinations |
|---|---|
| 15 | 1 2 3 4 5 |
| 16 | 1 2 3 4 6 |
| 17 | 1 2 3 4 71 2 3 5 6 |
| 18 | 1 2 3 4 81 2 3 5 71 2 4 5 6 |
| 19 | 1 2 3 4 91 2 3 5 81 2 3 6 71 2 4 5 71 3 4 5 6 |
| 20 | 1 2 3 5 91 2 3 6 81 2 4 5 81 2 4 6 71 3 4 5 72 3 4 5 6 |
| 21 | 1 2 3 6 91 2 3 7 81 2 4 5 91 2 4 6 81 2 5 6 71 3 4 5 81 3 4 6 72 3 4 5 7 |
| 22 | 1 2 3 7 91 2 4 6 91 2 4 7 81 2 5 6 81 3 4 5 91 3 4 6 81 3 5 6 72 3 4 5 82 3 4 6 7 |
| 23 | 1 2 3 8 91 2 4 7 91 2 5 6 91 2 5 7 81 3 4 6 91 3 4 7 81 3 5 6 81 4 5 6 72 3 4 5 92 3 4 6 82 3 5 6 7 |
| 24 | 1 2 4 8 91 2 5 7 91 2 6 7 81 3 4 7 91 3 5 6 91 3 5 7 81 4 5 6 82 3 4 6 92 3 4 7 82 3 5 6 82 4 5 6 7 |
| 25 | 1 2 5 8 91 2 6 7 91 3 4 8 91 3 5 7 91 3 6 7 81 4 5 6 91 4 5 7 82 3 4 7 92 3 5 6 92 3 5 7 82 4 5 6 83 4 5 6 7 |
| 26 | 1 2 6 8 91 3 5 8 91 3 6 7 91 4 5 7 91 4 6 7 82 3 4 8 92 3 5 7 92 3 6 7 82 4 5 6 92 4 5 7 83 4 5 6 8 |
| 27 | 1 2 7 8 91 3 6 8 91 4 5 8 91 4 6 7 91 5 6 7 82 3 5 8 92 3 6 7 92 4 5 7 92 4 6 7 83 4 5 6 93 4 5 7 8 |
| 28 | 1 3 7 8 91 4 6 8 91 5 6 7 92 3 6 8 92 4 5 8 92 4 6 7 92 5 6 7 83 4 5 7 93 4 6 7 8 |
| 29 | 1 4 7 8 91 5 6 8 92 3 7 8 92 4 6 8 92 5 6 7 93 4 5 8 93 4 6 7 93 5 6 7 8 |
| 30 | 1 5 7 8 92 4 7 8 92 5 6 8 93 4 6 8 93 5 6 7 94 5 6 7 8 |
| 31 | 1 6 7 8 92 5 7 8 93 4 7 8 93 5 6 8 94 5 6 7 9 |
| 32 | 2 6 7 8 93 5 7 8 94 5 6 8 9 |
| 33 | 3 6 7 8 94 5 7 8 9 |
| 34 | 4 6 7 8 9 |
| 35 | 5 6 7 8 9 |
6-cell cages sums 21–39
| Sum | Combinations |
|---|---|
| 21 | 1 2 3 4 5 6 |
| 22 | 1 2 3 4 5 7 |
| 23 | 1 2 3 4 5 81 2 3 4 6 7 |
| 24 | 1 2 3 4 5 91 2 3 4 6 81 2 3 5 6 7 |
| 25 | 1 2 3 4 6 91 2 3 4 7 81 2 3 5 6 81 2 4 5 6 7 |
| 26 | 1 2 3 4 7 91 2 3 5 6 91 2 3 5 7 81 2 4 5 6 81 3 4 5 6 7 |
| 27 | 1 2 3 4 8 91 2 3 5 7 91 2 3 6 7 81 2 4 5 6 91 2 4 5 7 81 3 4 5 6 82 3 4 5 6 7 |
| 28 | 1 2 3 5 8 91 2 3 6 7 91 2 4 5 7 91 2 4 6 7 81 3 4 5 6 91 3 4 5 7 82 3 4 5 6 8 |
| 29 | 1 2 3 6 8 91 2 4 5 8 91 2 4 6 7 91 2 5 6 7 81 3 4 5 7 91 3 4 6 7 82 3 4 5 6 92 3 4 5 7 8 |
| 30 | 1 2 3 7 8 91 2 4 6 8 91 2 5 6 7 91 3 4 5 8 91 3 4 6 7 91 3 5 6 7 82 3 4 5 7 92 3 4 6 7 8 |
| 31 | 1 2 4 7 8 91 2 5 6 8 91 3 4 6 8 91 3 5 6 7 91 4 5 6 7 82 3 4 5 8 92 3 4 6 7 92 3 5 6 7 8 |
| 32 | 1 2 5 7 8 91 3 4 7 8 91 3 5 6 8 91 4 5 6 7 92 3 4 6 8 92 3 5 6 7 92 4 5 6 7 8 |
| 33 | 1 2 6 7 8 91 3 5 7 8 91 4 5 6 8 92 3 4 7 8 92 3 5 6 8 92 4 5 6 7 93 4 5 6 7 8 |
| 34 | 1 3 6 7 8 91 4 5 7 8 92 3 5 7 8 92 4 5 6 8 93 4 5 6 7 9 |
| 35 | 1 4 6 7 8 92 3 6 7 8 92 4 5 7 8 93 4 5 6 8 9 |
| 36 | 1 5 6 7 8 92 4 6 7 8 93 4 5 7 8 9 |
| 37 | 2 5 6 7 8 93 4 6 7 8 9 |
| 38 | 3 5 6 7 8 9 |
| 39 | 4 5 6 7 8 9 |
7-cell cages sums 28–42
| Sum | Combinations |
|---|---|
| 28 | 1 2 3 4 5 6 7 |
| 29 | 1 2 3 4 5 6 8 |
| 30 | 1 2 3 4 5 6 91 2 3 4 5 7 8 |
| 31 | 1 2 3 4 5 7 91 2 3 4 6 7 8 |
| 32 | 1 2 3 4 5 8 91 2 3 4 6 7 91 2 3 5 6 7 8 |
| 33 | 1 2 3 4 6 8 91 2 3 5 6 7 91 2 4 5 6 7 8 |
| 34 | 1 2 3 4 7 8 91 2 3 5 6 8 91 2 4 5 6 7 91 3 4 5 6 7 8 |
| 35 | 1 2 3 5 7 8 91 2 4 5 6 8 91 3 4 5 6 7 92 3 4 5 6 7 8 |
| 36 | 1 2 3 6 7 8 91 2 4 5 7 8 91 3 4 5 6 8 92 3 4 5 6 7 9 |
| 37 | 1 2 4 6 7 8 91 3 4 5 7 8 92 3 4 5 6 8 9 |
| 38 | 1 2 5 6 7 8 91 3 4 6 7 8 92 3 4 5 7 8 9 |
| 39 | 1 3 5 6 7 8 92 3 4 6 7 8 9 |
| 40 | 1 4 5 6 7 8 92 3 5 6 7 8 9 |
| 41 | 2 4 5 6 7 8 9 |
| 42 | 3 4 5 6 7 8 9 |
8-cell cages sums 36–44
| Sum | Combinations |
|---|---|
| 36 | 1 2 3 4 5 6 7 8 |
| 37 | 1 2 3 4 5 6 7 9 |
| 38 | 1 2 3 4 5 6 8 9 |
| 39 | 1 2 3 4 5 7 8 9 |
| 40 | 1 2 3 4 6 7 8 9 |
| 41 | 1 2 3 5 6 7 8 9 |
| 42 | 1 2 4 5 6 7 8 9 |
| 43 | 1 3 4 5 6 7 8 9 |
| 44 | 2 3 4 5 6 7 8 9 |
9-cell cages sums 45–45
| Sum | Combinations |
|---|---|
| 45 | 1 2 3 4 5 6 7 8 9 |
Frequently asked questions
What is a killer sudoku cage?
A cage is the dotted-outline group of cells in a killer sudoku, with a small number in its corner giving the sum of those cells. The digits inside a cage must add up to that sum and, like the rest of sudoku, cannot repeat within the cage. This calculator lists every set of distinct digits 1–9 that fits a given cage sum and size.
How do you calculate killer sudoku combinations?
For a cage of n cells and sum S, you find every combination of n different digits from 1–9 that add up to S. For example, a 2-cell cage summing to 5 can only be {1,4} or {2,3}. This tool enumerates them instantly, and can narrow the list when you already know some digits are in or out of the cage.
What is the 45 rule in killer sudoku?
Every row, column and 3×3 box contains the digits 1–9 exactly once, so each sums to 45. If a set of cages fills a row, column or box except for one cell, that cell equals 45 minus the cage totals — a common way to crack the opening of a killer sudoku.
Which killer sudoku cages have only one combination?
There are 34 "forced" cages whose sum and size allow just one set of digits — for example a 2-cell cage of 3 is always {1,2}, and a 4-cell cage of 30 is always {6,7,8,9}. They are listed in the unique-combinations table above and are the fastest cages to fill in.
Is this killer sudoku calculator free?
Yes. It runs entirely in your browser with no sign-up and nothing uploaded. Enter a cage sum and number of cells to see every valid combination, or use the full reference table as a printable cheat sheet.