Killer Sudoku Calculator
Working a killer cage? Pick the cage size and its target sum below, and the calculator lists every possible combination of digits 1–9 — plus which digits every combination must include, and which can never appear. Underneath you’ll find the classic combination cheat sheet for 2-, 3- and 4-cell cages. No download, no sign-up.
How to use the calculator
- Choose the cage size — how many cells the dashed cage covers (2 to 9).
- Choose the sum — the little number printed in the cage’s corner. Only possible sums are listed.
- Read the combinations — every valid set of digits appears instantly; digits can’t repeat inside a cage.
- Watch the “must include / never contains” line — digits shared by all combinations (or missing from all) are your strongest clues.
Killer Sudoku combinations: 2-cell cages
Two-cell cages are the workhorses of killer solving — and the extreme sums are forced outright: 3 = {1,2}, 4 = {1,3}, 16 = {7,9}, 17 = {8,9}.
| Sum | # | 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 cage combinations
Three-cell cages are forced at 6 = {1,2,3}, 7 = {1,2,4}, 23 = {6,8,9} and 24 = {7,8,9} — pencil those in on sight.
| Sum | # | 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 cage combinations
Four-cell cages are forced at 10 = {1,2,3,4}, 11 = {1,2,3,5}, 29 = {5,7,8,9} and 30 = {6,7,8,9}. In between, the “must include / never contains” line in the calculator does the heavy lifting.
| Sum | # | 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 |
Bigger cages: the one-combination sums
For cages of five cells and up, the full lists get long — what matters at the table are the sums with exactly one combination. These are worth recognising on sight:
| Cage | Sums with only one combination |
|---|---|
| 5 cells | 15 = 1+2+3+4+5 · 16 = 1+2+3+4+6 · 34 = 4+6+7+8+9 · 35 = 5+6+7+8+9 |
| 6 cells | 21 = 1+2+3+4+5+6 · 22 = 1+2+3+4+5+7 · 38 = 3+5+6+7+8+9 · 39 = 4+5+6+7+8+9 |
| 7 cells | 28 = 1+2+3+4+5+6+7 · 29 = 1+2+3+4+5+6+8 · 41 = 2+4+5+6+7+8+9 · 42 = 3+4+5+6+7+8+9 |
| 8 cells | 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 cells | 45 = 1+2+3+4+5+6+7+8+9 |
Everything else is a job for the calculator above. And remember the rule of 45: every row, column and 3×3 box sums to 45, so a cage poking in or out of a box forces the odd cell by subtraction.
Put it to work
Cheat sheet in hand, play a board: the killer Sudoku page has the rules and strategy plus free easy and hard boards, and the daily killer Sudoku deals one shared puzzle a day. The same cage arithmetic powers Kakuro, if cross-sums are your thing.
Killer Sudoku Calculator: FAQ
What does the killer Sudoku calculator do?
Given a cage size (2–9 cells) and its target sum, it lists every possible combination of the digits 1–9 with no repeats — and highlights digits that every combination must include, or that none can contain.
Why can’t a digit repeat inside a cage?
It’s a core killer Sudoku rule: within one dashed cage each digit may appear at most once, on top of the usual row, column and box rules. That’s why a 2-cell cage summing to 4 must be {1,3} — 2+2 is not allowed.
What are the most useful combinations to memorise?
The forced ones: 2-cell cages 3, 4, 16, 17; 3-cell cages 6, 7, 23, 24; 4-cell cages 10, 11, 29, 30. Each of these has exactly one possible combination.
What is the rule of 45?
Every row, column and 3×3 box contains 1–9, which sums to 45. If cages almost fill a box, the leftover cell (an “innie”) or protruding cell (an “outie”) is found by subtracting the cage totals from 45.
Is the calculator free?
Yes — it runs free in your browser with no download and no sign-up, and works offline once the page is open.