Killer Sudoku reference
Killer Sudoku cheat sheet
Every set of digits that can fill a cage, for every cage size and every total. Use the calculator for the cage in front of you, or the tables below as the full printed-style reference — and start with the 34 totals that have only one possible answer, because those are what open a grid.
Cage calculator
Pick the number of cells and the total printed in the corner of the cage. Every combination that fits is listed — no cage on any killer grid falls outside this.
3 cells totalling 15 — 8 combinations
- 159
- 168
- 249
- 258
- 267
- 348
- 357
- 456
The 34 cages with only one answer
These are the ones worth knowing by heart. Each of these totals can be made exactly one way, so the moment you see one you can write its digits into the cage as a locked set without solving anything. Everything else on this page is a lookup; this part is memorisation, and it is about twenty minutes of it.
How to read the tables
A cage is the dotted outline on a killer grid with a small number in its top-left corner. The digits inside it must add up to that number and — this is the part that does the work — they must all be different, even when the cage bends across two boxes. So a five-cell cage totalling 16 is not “any five digits adding to 16”; it is one specific set, 1 2 3 4 6, and nothing else.
Find your cage size below, run down the Total column, and the row lists every set that fits. A row with one set is a placement. A row with two or three is still worth writing down as candidates, because the digits those sets have in common are forced — every two-cell cage totalling 5 contains either 1 4 or 2 3, so it never contains a 5, 6, 7, 8 or 9.
The rule of 45
Every row, column and box on a 9×9 grid holds the digits 1–9 exactly once, so each of them totals 45. That single fact is the other half of killer solving: add up the cages that sit wholly inside one box, subtract from 45, and whatever is left is the total of the cells that stick out. It routinely hands you a one-cell answer for free.
The same works across two or three boxes at once — three stacked boxes total 135 — which is how the awkward cages that straddle a boundary get cracked.
Where the cheat sheet stops helping
Cage combinations get you into a killer grid and rarely finish one. Once the cages have given up their sets you are solving an ordinary Sudoku with an unusually good set of starting candidates, and the rest is the same work as any hard board: hidden singles, naked pairs and, when it stalls, pointing pairs.
If the arithmetic side is new to you but the grid side is too, how to play Sudoku covers the underlying rules first — killer is standard Sudoku with sums added, not a different puzzle.
Every cage, by size
The complete table. Cages of seven, eight and nine cells are listed for completeness but are easier read backwards: an eight-cell cage is the whole set 1–9 with one digit missing, so its total is always 45 minus the digit that is not there.
2-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 3 | 1 | 12 |
| 4 | 1 | 13 |
| 5 | 2 | 1423 |
| 6 | 2 | 1524 |
| 7 | 3 | 162534 |
| 8 | 3 | 172635 |
| 9 | 4 | 18273645 |
| 10 | 4 | 19283746 |
| 11 | 4 | 29384756 |
| 12 | 3 | 394857 |
| 13 | 3 | 495867 |
| 14 | 2 | 5968 |
| 15 | 2 | 6978 |
| 16 | 1 | 79 |
| 17 | 1 | 89 |
3-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 6 | 1 | 123 |
| 7 | 1 | 124 |
| 8 | 2 | 125134 |
| 9 | 3 | 126135234 |
| 10 | 4 | 127136145235 |
| 11 | 5 | 128137146236245 |
| 12 | 7 | 129138147156237246345 |
| 13 | 7 | 139148157238247256346 |
| 14 | 8 | 149158167239248257347356 |
| 15 | 8 | 159168249258267348357456 |
| 16 | 8 | 169178259268349358367457 |
| 17 | 7 | 179269278359368458467 |
| 18 | 7 | 189279369378459468567 |
| 19 | 5 | 289379469478568 |
| 20 | 4 | 389479569578 |
| 21 | 3 | 489579678 |
| 22 | 2 | 589679 |
| 23 | 1 | 689 |
| 24 | 1 | 789 |
4-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 10 | 1 | 1234 |
| 11 | 1 | 1235 |
| 12 | 2 | 12361245 |
| 13 | 3 | 123712461345 |
| 14 | 5 | 12381247125613462345 |
| 15 | 6 | 123912481257134713562346 |
| 16 | 8 | 12491258126713481357145623472356 |
| 17 | 9 | 125912681349135813671457234823572456 |
| 18 | 11 | 12691278135913681458146723492358236724573456 |
| 19 | 11 | 12791369137814591468156723592368245824673457 |
| 20 | 12 | 128913791469147815682369237824592468256734583467 |
| 21 | 11 | 13891479156915782379246924782568345934683567 |
| 22 | 11 | 14891579167823892479256925783469347835684567 |
| 23 | 9 | 158916792489257926783479356935784568 |
| 24 | 8 | 16892589267934893579367845694578 |
| 25 | 6 | 178926893589367945794678 |
| 26 | 5 | 27893689458946795678 |
| 27 | 3 | 378946895679 |
| 28 | 2 | 47895689 |
| 29 | 1 | 5789 |
| 30 | 1 | 6789 |
5-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 15 | 1 | 12345 |
| 16 | 1 | 12346 |
| 17 | 2 | 1234712356 |
| 18 | 3 | 123481235712456 |
| 19 | 5 | 1234912358123671245713456 |
| 20 | 6 | 123591236812458124671345723456 |
| 21 | 8 | 1236912378124591246812567134581346723457 |
| 22 | 9 | 123791246912478125681345913468135672345823467 |
| 23 | 11 | 1238912479125691257813469134781356814567234592346823567 |
| 24 | 11 | 1248912579126781347913569135781456823469234782356824567 |
| 25 | 12 | 125891267913489135791367814569145782347923569235782456834567 |
| 26 | 11 | 1268913589136791457914678234892357923678245692457834568 |
| 27 | 11 | 1278913689145891467915678235892367924579246783456934578 |
| 28 | 9 | 137891468915679236892458924679256783457934678 |
| 29 | 8 | 1478915689237892468925679345893467935678 |
| 30 | 6 | 157892478925689346893567945678 |
| 31 | 5 | 1678925789347893568945679 |
| 32 | 3 | 267893578945689 |
| 33 | 2 | 3678945789 |
| 34 | 1 | 46789 |
| 35 | 1 | 56789 |
6-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 21 | 1 | 123456 |
| 22 | 1 | 123457 |
| 23 | 2 | 123458123467 |
| 24 | 3 | 123459123468123567 |
| 25 | 4 | 123469123478123568124567 |
| 26 | 5 | 123479123569123578124568134567 |
| 27 | 7 | 123489123579123678124569124578134568234567 |
| 28 | 7 | 123589123679124579124678134569134578234568 |
| 29 | 8 | 123689124589124679125678134579134678234569234578 |
| 30 | 8 | 123789124689125679134589134679135678234579234678 |
| 31 | 8 | 124789125689134689135679145678234589234679235678 |
| 32 | 7 | 125789134789135689145679234689235679245678 |
| 33 | 7 | 126789135789145689234789235689245679345678 |
| 34 | 5 | 136789145789235789245689345679 |
| 35 | 4 | 146789236789245789345689 |
| 36 | 3 | 156789246789345789 |
| 37 | 2 | 256789346789 |
| 38 | 1 | 356789 |
| 39 | 1 | 456789 |
7-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 28 | 1 | 1234567 |
| 29 | 1 | 1234568 |
| 30 | 2 | 12345691234578 |
| 31 | 2 | 12345791234678 |
| 32 | 3 | 123458912346791235678 |
| 33 | 3 | 123468912356791245678 |
| 34 | 4 | 1234789123568912456791345678 |
| 35 | 4 | 1235789124568913456792345678 |
| 36 | 4 | 1236789124578913456892345679 |
| 37 | 3 | 124678913457892345689 |
| 38 | 3 | 125678913467892345789 |
| 39 | 2 | 13567892346789 |
| 40 | 2 | 14567892356789 |
| 41 | 1 | 2456789 |
| 42 | 1 | 3456789 |
8-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 36 | 1 | 12345678 |
| 37 | 1 | 12345679 |
| 38 | 1 | 12345689 |
| 39 | 1 | 12345789 |
| 40 | 1 | 12346789 |
| 41 | 1 | 12356789 |
| 42 | 1 | 12456789 |
| 43 | 1 | 13456789 |
| 44 | 1 | 23456789 |
9-cell cages
| Total | Sets | Combinations |
|---|---|---|
| 45 | 1 | 123456789 |
Frequently asked questions
What is a killer Sudoku cheat sheet?
It is the list of every combination of digits that can fill a cage of a given size for a given total. Because the digits in a cage are all different, a total like 16 across two cells has exactly one answer — 7 and 9 — and knowing which totals are forced like that is most of what separates a fast killer solve from a slow one.
How many cage totals have only one possible combination?
Thirty-four, counting every cage size from two cells up to nine. They cluster at the extremes: the smallest and largest totals a cage can carry are always forced, because there is only one way to make them. The list on this page is the complete set.
Can digits repeat inside a killer Sudoku cage?
No. Every digit in a cage is different, even where the cage bends across two boxes or spans a row and a column. That constraint is what makes the combination tables useful — without it a total would tell you almost nothing.
What is the rule of 45 in killer Sudoku?
Every row, column and 3×3 box contains the digits 1 to 9 exactly once, so each totals 45. Add the cages sitting wholly inside one of those units, subtract from 45, and the remainder is the total of whatever cells stick out — which often resolves a single cell outright.
Does Action Sudoku have killer Sudoku?
Not yet — Action Sudoku is standard 9×9 Sudoku, solo, daily and live 1v1. This page is a reference, and the cage arithmetic on it is the same wherever you are playing killer.
Is this cage calculator free?
Yes, and there is nothing to sign up for. The combinations are computed in your browser as you pick the size and total, so nothing is sent anywhere.
Keep reading
Sharpen the classic side
Action Sudoku is standard 9×9 — solo, daily, and live 1v1 against a real opponent. The pattern-spotting that finishes a killer grid is the same pattern-spotting that wins a race. Free on iOS and Android.