Killer Sudoku
Combine ordinary Sudoku with cage sums.
Rules
Fill each row, column and box with 1 through 9. Digits in each outlined cage must add to its small total and must not repeat within the cage. A cage may cross a box boundary; its sum and no-repeat rule still apply.
A visual example
How to start
Begin with cages that have few combinations, then use row, column and box restrictions to narrow the order. Every full standard unit totals 45: if cages exactly cover eight cells of a row with a combined total of 39, the remaining cell is 6. Only subtract cages that cover the intended cells without gaps or double counting.
A mistake to avoid
A combination fixes a set of digits, not their positions. A cage totaling 10 does not automatically contain 1 and 9; check every allowed combination and the cage size.
Killer cage combinations
These are unordered sets of distinct digits. Check the cage size and sum, then use the grid to determine positions.
2-cell cages
| Sum | Count | Combinations |
|---|---|---|
| 3 | 1 | 1 + 2 |
| 4 | 1 | 1 + 3 |
| 5 | 2 | 1 + 4; 2 + 3 |
| 6 | 2 | 1 + 5; 2 + 4 |
| 7 | 3 | 1 + 6; 2 + 5; 3 + 4 |
| 8 | 3 | 1 + 7; 2 + 6; 3 + 5 |
| 9 | 4 | 1 + 8; 2 + 7; 3 + 6; 4 + 5 |
| 10 | 4 | 1 + 9; 2 + 8; 3 + 7; 4 + 6 |
| 11 | 4 | 2 + 9; 3 + 8; 4 + 7; 5 + 6 |
| 12 | 3 | 3 + 9; 4 + 8; 5 + 7 |
| 13 | 3 | 4 + 9; 5 + 8; 6 + 7 |
| 14 | 2 | 5 + 9; 6 + 8 |
| 15 | 2 | 6 + 9; 7 + 8 |
| 16 | 1 | 7 + 9 |
| 17 | 1 | 8 + 9 |
3-cell cages
| Sum | Count | Combinations |
|---|---|---|
| 6 | 1 | 1 + 2 + 3 |
| 7 | 1 | 1 + 2 + 4 |
| 8 | 2 | 1 + 2 + 5; 1 + 3 + 4 |
| 9 | 3 | 1 + 2 + 6; 1 + 3 + 5; 2 + 3 + 4 |
| 10 | 4 | 1 + 2 + 7; 1 + 3 + 6; 1 + 4 + 5; 2 + 3 + 5 |
| 11 | 5 | 1 + 2 + 8; 1 + 3 + 7; 1 + 4 + 6; 2 + 3 + 6; 2 + 4 + 5 |
| 12 | 7 | 1 + 2 + 9; 1 + 3 + 8; 1 + 4 + 7; 1 + 5 + 6; 2 + 3 + 7; 2 + 4 + 6; 3 + 4 + 5 |
| 13 | 7 | 1 + 3 + 9; 1 + 4 + 8; 1 + 5 + 7; 2 + 3 + 8; 2 + 4 + 7; 2 + 5 + 6; 3 + 4 + 6 |
| 14 | 8 | 1 + 4 + 9; 1 + 5 + 8; 1 + 6 + 7; 2 + 3 + 9; 2 + 4 + 8; 2 + 5 + 7; 3 + 4 + 7; 3 + 5 + 6 |
| 15 | 8 | 1 + 5 + 9; 1 + 6 + 8; 2 + 4 + 9; 2 + 5 + 8; 2 + 6 + 7; 3 + 4 + 8; 3 + 5 + 7; 4 + 5 + 6 |
| 16 | 8 | 1 + 6 + 9; 1 + 7 + 8; 2 + 5 + 9; 2 + 6 + 8; 3 + 4 + 9; 3 + 5 + 8; 3 + 6 + 7; 4 + 5 + 7 |
| 17 | 7 | 1 + 7 + 9; 2 + 6 + 9; 2 + 7 + 8; 3 + 5 + 9; 3 + 6 + 8; 4 + 5 + 8; 4 + 6 + 7 |
| 18 | 7 | 1 + 8 + 9; 2 + 7 + 9; 3 + 6 + 9; 3 + 7 + 8; 4 + 5 + 9; 4 + 6 + 8; 5 + 6 + 7 |
| 19 | 5 | 2 + 8 + 9; 3 + 7 + 9; 4 + 6 + 9; 4 + 7 + 8; 5 + 6 + 8 |
| 20 | 4 | 3 + 8 + 9; 4 + 7 + 9; 5 + 6 + 9; 5 + 7 + 8 |
| 21 | 3 | 4 + 8 + 9; 5 + 7 + 9; 6 + 7 + 8 |
| 22 | 2 | 5 + 8 + 9; 6 + 7 + 9 |
| 23 | 1 | 6 + 8 + 9 |
| 24 | 1 | 7 + 8 + 9 |
4-cell cages
| Sum | Count | Combinations |
|---|---|---|
| 10 | 1 | 1 + 2 + 3 + 4 |
| 11 | 1 | 1 + 2 + 3 + 5 |
| 12 | 2 | 1 + 2 + 3 + 6; 1 + 2 + 4 + 5 |
| 13 | 3 | 1 + 2 + 3 + 7; 1 + 2 + 4 + 6; 1 + 3 + 4 + 5 |
| 14 | 5 | 1 + 2 + 3 + 8; 1 + 2 + 4 + 7; 1 + 2 + 5 + 6; 1 + 3 + 4 + 6; 2 + 3 + 4 + 5 |
| 15 | 6 | 1 + 2 + 3 + 9; 1 + 2 + 4 + 8; 1 + 2 + 5 + 7; 1 + 3 + 4 + 7; 1 + 3 + 5 + 6; 2 + 3 + 4 + 6 |
| 16 | 8 | 1 + 2 + 4 + 9; 1 + 2 + 5 + 8; 1 + 2 + 6 + 7; 1 + 3 + 4 + 8; 1 + 3 + 5 + 7; 1 + 4 + 5 + 6; 2 + 3 + 4 + 7; 2 + 3 + 5 + 6 |
| 17 | 9 | 1 + 2 + 5 + 9; 1 + 2 + 6 + 8; 1 + 3 + 4 + 9; 1 + 3 + 5 + 8; 1 + 3 + 6 + 7; 1 + 4 + 5 + 7; 2 + 3 + 4 + 8; 2 + 3 + 5 + 7; 2 + 4 + 5 + 6 |
| 18 | 11 | 1 + 2 + 6 + 9; 1 + 2 + 7 + 8; 1 + 3 + 5 + 9; 1 + 3 + 6 + 8; 1 + 4 + 5 + 8; 1 + 4 + 6 + 7; 2 + 3 + 4 + 9; 2 + 3 + 5 + 8; 2 + 3 + 6 + 7; 2 + 4 + 5 + 7; 3 + 4 + 5 + 6 |
| 19 | 11 | 1 + 2 + 7 + 9; 1 + 3 + 6 + 9; 1 + 3 + 7 + 8; 1 + 4 + 5 + 9; 1 + 4 + 6 + 8; 1 + 5 + 6 + 7; 2 + 3 + 5 + 9; 2 + 3 + 6 + 8; 2 + 4 + 5 + 8; 2 + 4 + 6 + 7; 3 + 4 + 5 + 7 |
| 20 | 12 | 1 + 2 + 8 + 9; 1 + 3 + 7 + 9; 1 + 4 + 6 + 9; 1 + 4 + 7 + 8; 1 + 5 + 6 + 8; 2 + 3 + 6 + 9; 2 + 3 + 7 + 8; 2 + 4 + 5 + 9; 2 + 4 + 6 + 8; 2 + 5 + 6 + 7; 3 + 4 + 5 + 8; 3 + 4 + 6 + 7 |
| 21 | 11 | 1 + 3 + 8 + 9; 1 + 4 + 7 + 9; 1 + 5 + 6 + 9; 1 + 5 + 7 + 8; 2 + 3 + 7 + 9; 2 + 4 + 6 + 9; 2 + 4 + 7 + 8; 2 + 5 + 6 + 8; 3 + 4 + 5 + 9; 3 + 4 + 6 + 8; 3 + 5 + 6 + 7 |
| 22 | 11 | 1 + 4 + 8 + 9; 1 + 5 + 7 + 9; 1 + 6 + 7 + 8; 2 + 3 + 8 + 9; 2 + 4 + 7 + 9; 2 + 5 + 6 + 9; 2 + 5 + 7 + 8; 3 + 4 + 6 + 9; 3 + 4 + 7 + 8; 3 + 5 + 6 + 8; 4 + 5 + 6 + 7 |
| 23 | 9 | 1 + 5 + 8 + 9; 1 + 6 + 7 + 9; 2 + 4 + 8 + 9; 2 + 5 + 7 + 9; 2 + 6 + 7 + 8; 3 + 4 + 7 + 9; 3 + 5 + 6 + 9; 3 + 5 + 7 + 8; 4 + 5 + 6 + 8 |
| 24 | 8 | 1 + 6 + 8 + 9; 2 + 5 + 8 + 9; 2 + 6 + 7 + 9; 3 + 4 + 8 + 9; 3 + 5 + 7 + 9; 3 + 6 + 7 + 8; 4 + 5 + 6 + 9; 4 + 5 + 7 + 8 |
| 25 | 6 | 1 + 7 + 8 + 9; 2 + 6 + 8 + 9; 3 + 5 + 8 + 9; 3 + 6 + 7 + 9; 4 + 5 + 7 + 9; 4 + 6 + 7 + 8 |
| 26 | 5 | 2 + 7 + 8 + 9; 3 + 6 + 8 + 9; 4 + 5 + 8 + 9; 4 + 6 + 7 + 9; 5 + 6 + 7 + 8 |
| 27 | 3 | 3 + 7 + 8 + 9; 4 + 6 + 8 + 9; 5 + 6 + 7 + 9 |
| 28 | 2 | 4 + 7 + 8 + 9; 5 + 6 + 8 + 9 |
| 29 | 1 | 5 + 7 + 8 + 9 |
| 30 | 1 | 6 + 7 + 8 + 9 |
5-cell cages
| Sum | Count | Combinations |
|---|---|---|
| 15 | 1 | 1 + 2 + 3 + 4 + 5 |
| 16 | 1 | 1 + 2 + 3 + 4 + 6 |
| 17 | 2 | 1 + 2 + 3 + 4 + 7; 1 + 2 + 3 + 5 + 6 |
| 18 | 3 | 1 + 2 + 3 + 4 + 8; 1 + 2 + 3 + 5 + 7; 1 + 2 + 4 + 5 + 6 |
| 19 | 5 | 1 + 2 + 3 + 4 + 9; 1 + 2 + 3 + 5 + 8; 1 + 2 + 3 + 6 + 7; 1 + 2 + 4 + 5 + 7; 1 + 3 + 4 + 5 + 6 |
| 20 | 6 | 1 + 2 + 3 + 5 + 9; 1 + 2 + 3 + 6 + 8; 1 + 2 + 4 + 5 + 8; 1 + 2 + 4 + 6 + 7; 1 + 3 + 4 + 5 + 7; 2 + 3 + 4 + 5 + 6 |
| 21 | 8 | 1 + 2 + 3 + 6 + 9; 1 + 2 + 3 + 7 + 8; 1 + 2 + 4 + 5 + 9; 1 + 2 + 4 + 6 + 8; 1 + 2 + 5 + 6 + 7; 1 + 3 + 4 + 5 + 8; 1 + 3 + 4 + 6 + 7; 2 + 3 + 4 + 5 + 7 |
| 22 | 9 | 1 + 2 + 3 + 7 + 9; 1 + 2 + 4 + 6 + 9; 1 + 2 + 4 + 7 + 8; 1 + 2 + 5 + 6 + 8; 1 + 3 + 4 + 5 + 9; 1 + 3 + 4 + 6 + 8; 1 + 3 + 5 + 6 + 7; 2 + 3 + 4 + 5 + 8; 2 + 3 + 4 + 6 + 7 |
| 23 | 11 | 1 + 2 + 3 + 8 + 9; 1 + 2 + 4 + 7 + 9; 1 + 2 + 5 + 6 + 9; 1 + 2 + 5 + 7 + 8; 1 + 3 + 4 + 6 + 9; 1 + 3 + 4 + 7 + 8; 1 + 3 + 5 + 6 + 8; 1 + 4 + 5 + 6 + 7; 2 + 3 + 4 + 5 + 9; 2 + 3 + 4 + 6 + 8; 2 + 3 + 5 + 6 + 7 |
| 24 | 11 | 1 + 2 + 4 + 8 + 9; 1 + 2 + 5 + 7 + 9; 1 + 2 + 6 + 7 + 8; 1 + 3 + 4 + 7 + 9; 1 + 3 + 5 + 6 + 9; 1 + 3 + 5 + 7 + 8; 1 + 4 + 5 + 6 + 8; 2 + 3 + 4 + 6 + 9; 2 + 3 + 4 + 7 + 8; 2 + 3 + 5 + 6 + 8; 2 + 4 + 5 + 6 + 7 |
| 25 | 12 | 1 + 2 + 5 + 8 + 9; 1 + 2 + 6 + 7 + 9; 1 + 3 + 4 + 8 + 9; 1 + 3 + 5 + 7 + 9; 1 + 3 + 6 + 7 + 8; 1 + 4 + 5 + 6 + 9; 1 + 4 + 5 + 7 + 8; 2 + 3 + 4 + 7 + 9; 2 + 3 + 5 + 6 + 9; 2 + 3 + 5 + 7 + 8; 2 + 4 + 5 + 6 + 8; 3 + 4 + 5 + 6 + 7 |
| 26 | 11 | 1 + 2 + 6 + 8 + 9; 1 + 3 + 5 + 8 + 9; 1 + 3 + 6 + 7 + 9; 1 + 4 + 5 + 7 + 9; 1 + 4 + 6 + 7 + 8; 2 + 3 + 4 + 8 + 9; 2 + 3 + 5 + 7 + 9; 2 + 3 + 6 + 7 + 8; 2 + 4 + 5 + 6 + 9; 2 + 4 + 5 + 7 + 8; 3 + 4 + 5 + 6 + 8 |
| 27 | 11 | 1 + 2 + 7 + 8 + 9; 1 + 3 + 6 + 8 + 9; 1 + 4 + 5 + 8 + 9; 1 + 4 + 6 + 7 + 9; 1 + 5 + 6 + 7 + 8; 2 + 3 + 5 + 8 + 9; 2 + 3 + 6 + 7 + 9; 2 + 4 + 5 + 7 + 9; 2 + 4 + 6 + 7 + 8; 3 + 4 + 5 + 6 + 9; 3 + 4 + 5 + 7 + 8 |
| 28 | 9 | 1 + 3 + 7 + 8 + 9; 1 + 4 + 6 + 8 + 9; 1 + 5 + 6 + 7 + 9; 2 + 3 + 6 + 8 + 9; 2 + 4 + 5 + 8 + 9; 2 + 4 + 6 + 7 + 9; 2 + 5 + 6 + 7 + 8; 3 + 4 + 5 + 7 + 9; 3 + 4 + 6 + 7 + 8 |
| 29 | 8 | 1 + 4 + 7 + 8 + 9; 1 + 5 + 6 + 8 + 9; 2 + 3 + 7 + 8 + 9; 2 + 4 + 6 + 8 + 9; 2 + 5 + 6 + 7 + 9; 3 + 4 + 5 + 8 + 9; 3 + 4 + 6 + 7 + 9; 3 + 5 + 6 + 7 + 8 |
| 30 | 6 | 1 + 5 + 7 + 8 + 9; 2 + 4 + 7 + 8 + 9; 2 + 5 + 6 + 8 + 9; 3 + 4 + 6 + 8 + 9; 3 + 5 + 6 + 7 + 9; 4 + 5 + 6 + 7 + 8 |
| 31 | 5 | 1 + 6 + 7 + 8 + 9; 2 + 5 + 7 + 8 + 9; 3 + 4 + 7 + 8 + 9; 3 + 5 + 6 + 8 + 9; 4 + 5 + 6 + 7 + 9 |
| 32 | 3 | 2 + 6 + 7 + 8 + 9; 3 + 5 + 7 + 8 + 9; 4 + 5 + 6 + 8 + 9 |
| 33 | 2 | 3 + 6 + 7 + 8 + 9; 4 + 5 + 7 + 8 + 9 |
| 34 | 1 | 4 + 6 + 7 + 8 + 9 |
| 35 | 1 | 5 + 6 + 7 + 8 + 9 |
Keep learning
Review the standard rules and worked solving techniques. Our daily game and printable packs use standard Sudoku rules; they do not play this variant.