Killer sudoku is the variant that adds arithmetic to the classic grid — and, in a twist beginners rarely expect, usually starts with no given digits at all. Instead of clues, the board is carved into outlined groups of cells called cages, each printed with a small number: the sum its cells must reach. Everything else you know still applies, which is exactly what makes the variant approachable. This guide covers the rules, the one technique that unlocks most grids, and where the puzzle came from.
The rules, in full
Three constraints govern every killer grid, and two of them are old friends:
- Classic sudoku holds. Every row, column and 3×3 box contains the digits 1–9 exactly once — the same single rule explained in the sudoku rules guide.
- Each cage must hit its printed sum. A three-cell cage marked 7 must hold three digits adding to exactly 7.
- No digit repeats inside a cage. That cage marked 7 cannot be 1+3+3; it must be 1+2+4, the only combination left.
That third rule is the quiet engine of the whole variant: it cuts the possible digit combinations for each sum down dramatically, and reading cages as short lists of combinations is what solving killer actually feels like.
Cage arithmetic: the combination lists
Some sums pin their cages down completely. A two-cell cage marked 3 can only be 1+2; marked 17, only 8+9. A three-cell cage marked 6 must be 1+2+3, and marked 24 must be 7+8+9. These forced cages are where every grid starts: find them, pencil in their few candidates, and let the classic row-column-box logic take over from there. Middling sums are looser — a two-cell 10 could be 1+9, 2+8, 3+7 or 4+6 — so you work the extremes first and return to the flexible cages once the board has tightened around them.
The 45 rule, the variant’s signature move
Because a complete row, column or box holds 1 through 9, its nine cells always sum to 45. That fixed total turns the printed cage sums into a measuring tool. If the cages lying entirely inside one box add up to 38, and exactly one cell of that box belongs to a cage poking outside, that cell’s whole cage contribution is pinned by the difference. Solvers call these innies and outies: the single cell sticking into a region, or out of it, whose value is forced by subtracting cage sums from 45. On many killer grids the first several digits arrive this way before any classic technique fires at all.
A worked opening, in words
Picture a corner box whose cages are: a two-cell 4, a three-cell 24, and a four-cell cage reaching one cell into the neighbouring box. The two-cell 4 must be 1+3. The 24 must be 7+8+9. Together they account for 28 of the box’s 45, leaving 17 for the remaining four cells — three of which sit in the four-cell cage. If that cage is marked 21, its outside cell holds 21 minus 17: a 4, written down before a single classic clue was touched. Every killer opening is a chain of exactly this shape.
After the opening: back to classic logic
Once the forced cages and the 45-rule deductions have seeded the board, killer behaves like a normal grid with unusually good pencil marks. Naked and hidden singles appear, pairs prune candidates, and on hard boards the advanced patterns from the techniques guide earn their keep. The rhythm alternates: arithmetic tightens the cages, placement logic fills the cells, and each side feeds the other until the grid closes. If the base game itself is new to you, the beginner walkthrough is the place to start before adding sums on top.
Where killer sudoku comes from
The variant is Japanese, like the modern history of the base puzzle itself. It grew from an idea credited to Miyuki Nisawa, developed by the Tokyo puzzle setter Tetsuya Nishio, and circulates in Japan under the name samunamupure — «sum number place», a nod to the original Number Place name that sudoku itself once carried. Outside Japan it arrived when The Times of London began printing the puzzle in 2005, riding the same wave that made the classic grid a newspaper fixture, and the «killer» label stuck for the extra bite the sums add.
Frequently asked questions
What are the rules of killer sudoku?
Classic sudoku rules apply — digits 1–9 once per row, column and box — plus two more: the cells of each outlined cage must add up to the printed sum, and no digit may repeat within a cage.
Why does killer sudoku have no starting numbers?
The cage sums replace the givens. Forced cages (like a two-cell 3 or 17) and the 45 rule provide the first placements, after which ordinary sudoku logic carries the grid.
What is the 45 rule in killer sudoku?
Every row, column and box sums to 45, because it holds 1 through 9 exactly once. Comparing that fixed total against the printed cage sums forces the value of cells that stick into or out of a region.
Is killer sudoku harder than regular sudoku?
It is different rather than strictly harder: the opening leans on arithmetic instead of scanning, which beginners find unfamiliar, but the cage sums also act as extra clues once you learn to read them.
