Killer sudoku combinations chart
Every valid digit combination for killer sudoku cages, organized by cage size and target sum. Use this as a quick reference while solving. Digits 1 through 9, no repeats within a cage.
How to use this chart
Find your cage size (number of cells), then find the target sum. The listed combinations show every possible set of digits. When solving, cross out any combination that includes a digit already placed in the same row, column, or box as one of the cage cells. If only one combination survives, all its digits are confirmed for that cage.
Forced combinations (only one valid option) are the fastest way to fill cells in killer sudoku. Two-cell cages with sum 3 (always 1+2), sum 4 (always 1+3), sum 16 (always 7+9), and sum 17 (always 8+9) are the most common.
2-cell cages
| Sum | Combinations | # |
|---|---|---|
| 3 | 1+2 | 1 |
| 4 | 1+3 | 1 |
| 5 | 1+42+3 | 2 |
| 6 | 1+52+4 | 2 |
| 7 | 1+62+53+4 | 3 |
| 8 | 1+72+63+5 | 3 |
| 9 | 1+82+73+64+5 | 4 |
| 10 | 1+92+83+74+6 | 4 |
| 11 | 2+93+84+75+6 | 4 |
| 12 | 3+94+85+7 | 3 |
| 13 | 4+95+86+7 | 3 |
| 14 | 5+96+8 | 2 |
| 15 | 6+97+8 | 2 |
| 16 | 7+9 | 1 |
| 17 | 8+9 | 1 |
3-cell cages
| Sum | Combinations | # |
|---|---|---|
| 6 | 1+2+3 | 1 |
| 7 | 1+2+4 | 1 |
| 8 | 1+2+51+3+4 | 2 |
| 9 | 1+2+61+3+52+3+4 | 3 |
| 10 | 1+2+71+3+61+4+52+3+5 | 4 |
| 11 | 1+2+81+3+71+4+62+3+62+4+5 | 5 |
| 12 | 1+2+91+3+81+4+71+5+62+3+72+4+63+4+5 | 7 |
| 13 | 1+3+91+4+81+5+72+3+82+4+72+5+63+4+6 | 7 |
| 14 | 1+4+91+5+81+6+72+3+92+4+82+5+73+4+73+5+6 | 8 |
| 15 | 1+5+91+6+82+4+92+5+82+6+73+4+83+5+74+5+6 | 8 |
| 16 | 1+6+91+7+82+5+92+6+83+4+93+5+83+6+74+5+7 | 8 |
| 17 | 1+7+92+6+92+7+83+5+93+6+84+5+84+6+7 | 7 |
| 18 | 1+8+92+7+93+6+93+7+84+5+94+6+85+6+7 | 7 |
| 19 | 2+8+93+7+94+6+94+7+85+6+8 | 5 |
| 20 | 3+8+94+7+95+6+95+7+8 | 4 |
| 21 | 4+8+95+7+96+7+8 | 3 |
| 22 | 5+8+96+7+9 | 2 |
| 23 | 6+8+9 | 1 |
| 24 | 7+8+9 | 1 |
4-cell cages
| Sum | Combinations | # |
|---|---|---|
| 10 | 1+2+3+4 | 1 |
| 11 | 1+2+3+5 | 1 |
| 12 | 1+2+3+61+2+4+5 | 2 |
| 13 | 1+2+3+71+2+4+61+3+4+5 | 3 |
| 14 | 1+2+3+81+2+4+71+2+5+61+3+4+62+3+4+5 | 5 |
| 15 | 1+2+3+91+2+4+81+2+5+71+3+4+71+3+5+62+3+4+6 | 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 | 8 |
| 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 | 9 |
| 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 | 11 |
| 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 | 11 |
| 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 | 12 |
| 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 | 11 |
| 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 | 11 |
| 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 | 9 |
| 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 | 8 |
| 25 | 1+7+8+92+6+8+93+5+8+93+6+7+94+5+7+94+6+7+8 | 6 |
| 26 | 2+7+8+93+6+8+94+5+8+94+6+7+95+6+7+8 | 5 |
| 27 | 3+7+8+94+6+8+95+6+7+9 | 3 |
| 28 | 4+7+8+95+6+8+9 | 2 |
| 29 | 5+7+8+9 | 1 |
| 30 | 6+7+8+9 | 1 |
5-cell cages
| Sum | Combinations | # |
|---|---|---|
| 15 | 1+2+3+4+5 | 1 |
| 16 | 1+2+3+4+6 | 1 |
| 17 | 1+2+3+4+71+2+3+5+6 | 2 |
| 18 | 1+2+3+4+81+2+3+5+71+2+4+5+6 | 3 |
| 19 | 1+2+3+4+91+2+3+5+81+2+3+6+71+2+4+5+71+3+4+5+6 | 5 |
| 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 | 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 | 8 |
| 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 | 9 |
| 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 | 11 |
| 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 | 11 |
| 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 | 12 |
| 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 | 11 |
| 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 | 11 |
| 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 | 9 |
| 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 | 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 | 6 |
| 31 | 1+6+7+8+92+5+7+8+93+4+7+8+93+5+6+8+94+5+6+7+9 | 5 |
| 32 | 2+6+7+8+93+5+7+8+94+5+6+8+9 | 3 |
| 33 | 3+6+7+8+94+5+7+8+9 | 2 |
| 34 | 4+6+7+8+9 | 1 |
| 35 | 5+6+7+8+9 | 1 |
6-cell cages
| Sum | Combinations | # |
|---|---|---|
| 21 | 1+2+3+4+5+6 | 1 |
| 22 | 1+2+3+4+5+7 | 1 |
| 23 | 1+2+3+4+5+81+2+3+4+6+7 | 2 |
| 24 | 1+2+3+4+5+91+2+3+4+6+81+2+3+5+6+7 | 3 |
| 25 | 1+2+3+4+6+91+2+3+4+7+81+2+3+5+6+81+2+4+5+6+7 | 4 |
| 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 | 5 |
| 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 | 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 | 7 |
| 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 | 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 | 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 | 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 | 7 |
| 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 | 7 |
| 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 | 5 |
| 35 | 1+4+6+7+8+92+3+6+7+8+92+4+5+7+8+93+4+5+6+8+9 | 4 |
| 36 | 1+5+6+7+8+92+4+6+7+8+93+4+5+7+8+9 | 3 |
| 37 | 2+5+6+7+8+93+4+6+7+8+9 | 2 |
| 38 | 3+5+6+7+8+9 | 1 |
| 39 | 4+5+6+7+8+9 | 1 |
7-cell cages
| Sum | Combinations | # |
|---|---|---|
| 28 | 1+2+3+4+5+6+7 | 1 |
| 29 | 1+2+3+4+5+6+8 | 1 |
| 30 | 1+2+3+4+5+6+91+2+3+4+5+7+8 | 2 |
| 31 | 1+2+3+4+5+7+91+2+3+4+6+7+8 | 2 |
| 32 | 1+2+3+4+5+8+91+2+3+4+6+7+91+2+3+5+6+7+8 | 3 |
| 33 | 1+2+3+4+6+8+91+2+3+5+6+7+91+2+4+5+6+7+8 | 3 |
| 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 | 4 |
| 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 | 4 |
| 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 | 4 |
| 37 | 1+2+4+6+7+8+91+3+4+5+7+8+92+3+4+5+6+8+9 | 3 |
| 38 | 1+2+5+6+7+8+91+3+4+6+7+8+92+3+4+5+7+8+9 | 3 |
| 39 | 1+3+5+6+7+8+92+3+4+6+7+8+9 | 2 |
| 40 | 1+4+5+6+7+8+92+3+5+6+7+8+9 | 2 |
| 41 | 2+4+5+6+7+8+9 | 1 |
| 42 | 3+4+5+6+7+8+9 | 1 |
8-cell cages
| Sum | Combinations | # |
|---|---|---|
| 36 | 1+2+3+4+5+6+7+8 | 1 |
| 37 | 1+2+3+4+5+6+7+9 | 1 |
| 38 | 1+2+3+4+5+6+8+9 | 1 |
| 39 | 1+2+3+4+5+7+8+9 | 1 |
| 40 | 1+2+3+4+6+7+8+9 | 1 |
| 41 | 1+2+3+5+6+7+8+9 | 1 |
| 42 | 1+2+4+5+6+7+8+9 | 1 |
| 43 | 1+3+4+5+6+7+8+9 | 1 |
| 44 | 2+3+4+5+6+7+8+9 | 1 |
9-cell cages
| Sum | Combinations | # |
|---|---|---|
| 45 | 1+2+3+4+5+6+7+8+9 | 1 |