Killer Sudoku Puzzles
Ordinary sudoku rules, plus dashed cages that each show the total of the digits inside them — and no digit repeats within a cage. Every grid here is checked before you see it: exactly one solution, and solvable by reasoning alone.
Also known as sumdoku, sum sudoku and samunamupure.
Related Practice
What Is Killer Sudoku?
Killer sudoku is ordinary sudoku with arithmetic layered on top. Every row, column and 3×3 box still holds the digits 1 to 9 exactly once. The grid is also divided into cages — dashed outlines, each printed with a small number in its corner — and the digits inside a cage must add up to that number. Crucially, no digit may repeat inside a cage.
In its purest form a killer sudoku starts completely empty, with the cage sums as the only clues. That is why it feels so different from ordinary sudoku: you are not eliminating from given digits, you are deducing digits from sums.
The Rule Of 45
This is the technique that defines the puzzle, and it follows from something you already know. Every row, column and box contains 1 through 9 exactly once, so every one of them totals 45.
That turns cages into a measuring device. If a group of cages fills a box completely except for one cell, that cell must contain 45 minus the total of those cages. If a cage pokes one cell out of a box, that cell holds the cage total minus 45 subtracted the other way round. People call these innies and outies, and finding one usually unlocks a whole region.
Cages That Can Only Be Made One Way
Because a cage cannot repeat a digit, extreme sums are forced. These are worth memorising — they hand you digits before any sudoku reasoning at all.
| Cells | Sum | Only combination |
|---|---|---|
| 2 | 3 | 1 + 2 |
| 2 | 4 | 1 + 3 |
| 2 | 16 | 7 + 9 |
| 2 | 17 | 8 + 9 |
| 3 | 6 | 1 + 2 + 3 |
| 3 | 7 | 1 + 2 + 4 |
| 3 | 23 | 6 + 8 + 9 |
| 3 | 24 | 7 + 8 + 9 |
| 4 | 10 | 1 + 2 + 3 + 4 |
| 4 | 30 | 6 + 7 + 8 + 9 |
The Rule People Carry Over Wrongly
If you have played calcudoku, unlearn one thing: a killer sudoku cage never repeats a digit. In calcudoku a cage may hold the same number twice provided the cells are in different rows and columns; here it may not, ever. A two-cell cage summing to 10 cannot be 5 and 5, and forgetting that is the single commonest way to convince yourself a good grid is broken.
Why These Grids Start With Some Digits
Worth being straight about, because it is a departure from the purest form of the puzzle. The classic killer sudoku starts empty. Generating an empty grid that is both uniquely solvable and solvable without guessing turns out to be far slower than a page load allows — in testing, roughly one carving in thirty qualified, which works out at around thirty-eight seconds per puzzle.
| Given digits | Build rate | Time per puzzle |
|---|---|---|
| None | about 3% | ~38 seconds — unusable |
| 8 | 100% | ~32 milliseconds |
| 14 | 100% | ~2 milliseconds |
| 26 | 100% | under a millisecond |
So the grids here carry between eight and twenty-six givens depending on difficulty. The alternative was to make you wait, or to ship a grid with two solutions — and a puzzle with two answers is not a puzzle. The Sparse family, at eight givens, is as close to the classic form as this can honestly get.
How The No-Guess Promise Is Checked
Every grid passes two machine checks before it reaches you.
| Guarantee | How it is checked | If it fails |
|---|---|---|
| Exactly one solution | A backtracking solver counts solutions, stopping at two. | Discarded; a different grid is generated. |
| No guessing required | A second solver, restricted to human techniques, must finish unaided. | Discarded, never shown. |
That second solver is what Show me the next move replays: one deduction, with the reason — which cell, which digit, and which cage or box forced it. Then it stops and hands the grid back to you. A solve button answers the puzzle; this is meant to teach it.
Killer Sudoku Puzzles Frequently Asked Questions
What is killer sudoku?
A sudoku variant that adds arithmetic. The usual rules still apply — every row, column and 3x3 box contains the digits 1 to 9 exactly once — and the grid is also divided into dashed outlines called cages. Each cage shows the total of the digits inside it, and no digit may repeat within a cage. The classic form starts with no given numbers at all, clued entirely by the cage sums.
Can a digit repeat inside a killer sudoku cage?
No. Unlike calcudoku, where repeats are allowed as long as they are not in the same row or column, a killer sudoku cage never contains the same digit twice. That is why a two-cell cage summing to 10 cannot be 5 and 5, and it removes a large number of combinations that would otherwise be possible.
Why do the puzzles here start with some numbers filled in?
Because of a limit worth being straight about. The purest killer sudoku starts completely empty, but generating an empty grid that is both uniquely solvable and solvable without guessing takes far longer than a page load allows — in testing, about one carving in thirty qualified. Rather than make you wait, or ship a puzzle with two solutions, the grids here carry between eight and twenty-six given digits depending on difficulty.
Do these puzzles ever need a guess?
No, and that is checked rather than claimed. Before any grid is shown, a solver restricted to techniques a person could use must finish it unaided, and a second solver must confirm there is exactly one solution. A grid failing either check is discarded and a different one generated.
How do you solve killer sudoku?
Start with the cages whose total allows only one set of digits — a two-cell cage totalling 17 can only be 8 and 9 — because those give you certain numbers to build from. Then use the rule of 45, and fall back on ordinary sudoku elimination once enough digits are placed.
What is the rule of 45 in killer sudoku?
Every row, column and 3×3 box holds the digits 1 to 9 exactly once, so each of them totals 45. When the cages inside one box account for all but a single cell, that cell must be 45 minus the cage totals — which is often the first digit you can place.
Is killer sudoku harder than normal sudoku?
Usually, because it starts with far fewer given digits and the cage arithmetic has to do the work instead. The puzzles here carry between 8 and 26 givens depending on difficulty, which is what keeps every one of them solvable by reasoning alone.