Play Killer Sudoku Online
Sudoku meets Kakuro — fill the 9×9 grid using cage sum clues with 4 difficulty levels. Notes, undo & error checking — all free.
Created by Brian Hamilton
Select a cell and enter a number
How to play Killer Sudoku
All the ordinary Sudoku rules apply: every row, every column and every 3×3 box holds the digits 1 to 9 exactly once.
- The dashed outlines are cages. The small number gives the total its digits must add to.
- No digit may repeat inside a cage, even where the sudoku rules would allow it.
- There are no starting digits — the cages are the whole clue set.
- Every row, column and box totals 45, which is often more useful than any single cage.
Controls: tap a square and type or tap a digit. Notes lets you pencil in candidates, which is how most of the middle game is solved.
Sixteen cage sums name their digits outright
A Killer Sudoku cage gives a total and nothing else. For most totals that leaves plenty of options — but for certain combinations of cage size and total there is exactly one set of digits that works, and those are the cages to attack first.
Across cages of two to five squares there are 76 possible totals in all, and 16 of them fix their digits completely. The pattern is easy to hold: for every cage size it is the two lowest totals and the two highest.
| Squares | Total | The only digits that work |
|---|---|---|
| 2 | 3 | 1 2 |
| 4 | 1 3 | |
| 16 | 7 9 | |
| 17 | 8 9 | |
| 3 | 6 | 1 2 3 |
| 7 | 1 2 4 | |
| 23 | 6 8 9 | |
| 24 | 7 8 9 | |
| 4 | 10 | 1 2 3 4 |
| 11 | 1 2 3 5 | |
| 29 | 5 7 8 9 | |
| 30 | 6 7 8 9 | |
| 5 | 15 | 1 2 3 4 5 |
| 16 | 1 2 3 4 6 | |
| 34 | 4 6 7 8 9 | |
| 35 | 5 6 7 8 9 |
Knowing the digits is not the same as knowing the order, but it is most of the way there — especially when the cage crosses a row or box that already has some of those digits spoken for.
The rule of 45
Every row, column and 3×3 box holds the digits 1 to 9 exactly once, so each of them totals 45. That single number turns cage arithmetic into a lever on whole regions of the grid.
The standard use: take a box, add up the cages lying entirely inside it, and the difference from 45 is the total of whatever spills over the edge. If a box contains cages of 12, 9 and 16 and one square belonging to a cage that reaches outside, that square is 45 − 37 = 8.
It works the same way across two or three boxes at once, which is where it earns its keep on hard grids: three stacked boxes total 135, and the cages that stick out of them are pinned by the difference.
A worked board
Here is a medium grid from the generator on this page. There are no starting digits at all — the cages are the entire clue set.
Difficulty is cage size, and it changes what works
The setting does not hide digits — there are none to hide. It changes the shape of the cages, and that decides which techniques are available to you.
| Difficulty | Cages | Single squares | Cages with a pinned total |
|---|---|---|---|
| Easy | 59 | 37 | 66% |
| Medium | 38 | 8 | 24% |
| Hard | 32 | 6 | 23% |
| Expert | 28 | 5 | 21% |
Look at the easy row. Thirty-seven of its fifty-nine cages are single squares — which is to say the puzzle simply tells you those digits, and easy Killer Sudoku is much closer to ordinary Sudoku than to the puzzle above. From medium onwards the single squares nearly vanish and cages grow to four and five, where the pinned-total table stops carrying you and the rule of 45 takes over.
Where solvers get stuck
Letting a cage repeat a digit. No digit may appear twice within one cage, even where the cage bends across two rows and the sudoku rules would allow it. This is the opposite of KenKen, where cages may repeat, and swapping between the two puzzles is where the mistake usually creeps in.
Working cages without working regions. A cage total is a local fact. The rule of 45 is what connects cages to each other, and most stalls come from adding within cages when the next step was to add across a box.
Forgetting the ordinary sudoku rules still apply. Rows, columns and boxes constrain every square exactly as usual. A cage narrowed to two possible digits is often settled by a plain sudoku elimination rather than more arithmetic.
Two things you can check about these puzzles
Easy and medium puzzles are verified to have exactly one solution. A cage layout is only accepted once a solver has confirmed a single filling satisfies it, and if a layout cannot be confirmed it is discarded and another is generated. On hard and expert that confirmation frequently runs out of time, and those boards can admit more than one valid grid. The win check tests the rules rather than a stored answer, so any correct filling is accepted — but it is an honest limit rather than a feature.
The cage totals always add to 405. Every square belongs to exactly one cage, and the whole grid holds nine copies each of 1 to 9, so all the cage totals together come to 9 × 45 = 405. Adding them up is a quick way to confirm you have read every clue correctly before you start.
Killer Sudoku, Samunamupure and Sumdoku
Killer Sudoku is also published as Sumdoku, Sum Sudoku, Addoku and, in Japan, Samunamupure — a rendering of “sum number place”. It reached a wide English-speaking audience through British newspapers in the mid-2000s, following the Sudoku boom.
It is a strict superset of Sudoku: every ordinary sudoku rule still applies, with cage sums added on top and the starting digits taken away. That is why a Killer grid can begin completely empty and still have exactly one answer.
More number puzzles
If you like sums doing the deducing, try these: