Killer Sudoku: Rules and How to Solve It
Killer Sudoku blends classic Sudoku logic with simple arithmetic. It looks intimidating because of the dotted "cages" and little numbers, but once you learn how cages and sums work, it's one of the most rewarding Sudoku variants to solve. This guide covers everything from the basic rules to the combination tricks expert solvers rely on.
What is Killer Sudoku?
Killer Sudoku is a 9×9 grid that follows all the normal Sudoku rules: every row, column, and 3×3 box must contain the digits 1–9 exactly once. The twist is that the grid is also divided into dotted-outline regions called cages. Each cage shows a small target number in its corner — the digits inside that cage must add up to that sum, and no digit may repeat within a cage.
Cages and Sums
A cage can be any shape and size. A two-cell cage with a "4" means those two cells contain digits that add to 4 — so either 1 and 3 (not 2 and 2, since digits can't repeat in a cage). Crucially, Killer Sudoku puzzles usually start with no given numbers at all — the cage sums are your only clues, which is what makes the variant so satisfying.
The Rule of 45
Every row, column, and 3×3 box contains the digits 1 through 9, which always add up to 45. This is your most powerful tool. If cages neatly fill a box except for one cell, subtract the cage sums from 45 to find that cell's exact value. The same trick works across rows and columns, and even across groups of boxes.
Cage Combination Tricks
Some sums have only one possible combination, and these are gold:
- Two cells summing to 3 → only {1, 2}
- Two cells summing to 4 → only {1, 3}
- Two cells summing to 16 → only {7, 9}
- Two cells summing to 17 → only {8, 9}
- Three cells summing to 6 → only {1, 2, 3}
- Three cells summing to 24 → only {7, 8, 9}
Locking in these forced combinations early dramatically narrows candidates across the whole grid.
A Solving Strategy That Works
Start by marking every cage's possible combinations, prioritizing the unique ones above. Then apply the rule of 45 to fully or nearly-full boxes to pin down single cells. From there, switch to standard Sudoku techniques — naked pairs, hidden singles, and pointing pairs — using the cage constraints to eliminate candidates. Alternate between arithmetic (cage sums) and logic (row/column/box) until the grid resolves.
Killer vs. Classic Sudoku
If you can solve hard classic Sudoku, you already have most of the skills for Killer Sudoku — you just add arithmetic on top. Want to sharpen the logic side first? Our advanced strategies guide covers X-Wing, Swordfish, and forcing chains that carry straight over to Killer puzzles.