Killer Sudoku takes the classic 9×9 grid and adds a twist: irregular "cages" with sum constraints replace starting digits as the entry point for solving. This guide covers the rules, the essential cage combinations, and the techniques that make Killer puzzles solvable. For other variants, see our Sudoku Variants overview.
Killer Sudoku — sometimes called "Sumdoku" or "Addoku" — was invented in 1997 by Tetsuya Nishio and gained worldwide popularity through publications like The Times of London. The puzzle uses the same 9×9 grid as classic Sudoku, but cells are grouped into cages outlined by dotted lines. Each cage has a small number printed in one corner: that number is the sum of the digits inside the cage.
To solve, you must satisfy three rules simultaneously: every row, column, and 3×3 box contains digits 1–9 exactly once; the digits inside each cage add to the printed sum; and no digit repeats within a single cage. Most Killer puzzles have no starting digits at all — the cage sums alone constrain the solution to be unique.
The third rule is what distinguishes Killer from a simple sum puzzle. It often does more work than the first two combined, because it sharply limits which combinations of digits can fill a cage of a given size and sum.
Every row, column, and 3×3 box must total 1+2+3+4+5+6+7+8+9 = 45. This fixed sum is the engine behind Killer Sudoku's most powerful technique.
When cages within a unit cover all but one cell, that one cell is an innie. Its value is 45 minus the sum of all cages fully inside the unit. When a cage extends one cell outside the unit, that protruding cell is an outie, computed as the sum of all relevant cages minus 45. Innies and outies routinely crack open Killer puzzles that would otherwise require complex chain reasoning.
Many cage sums have only one possible combination of digits. Memorizing these unlocks fast solving. Here are the most useful starting points:
| Cage Size | Sum | Only Possible Combination |
|---|---|---|
| 2 cells | 3 | {1,2} |
| 2 cells | 4 | {1,3} |
| 2 cells | 16 | {7,9} |
| 2 cells | 17 | {8,9} |
| 3 cells | 6 | {1,2,3} |
| 3 cells | 7 | {1,2,4} |
| 3 cells | 23 | {6,8,9} |
| 3 cells | 24 | {7,8,9} |
| 4 cells | 10 | {1,2,3,4} |
| 4 cells | 30 | {6,7,8,9} |
The general pattern: very low sums and very high sums force unique combinations because they must use the smallest or largest digits. Mid-range sums (like a 3-cell cage summing to 15) have many possible combinations and require additional logic to narrow down.
A reliable solving order for Killer Sudoku:
| Feature | Classic Sudoku | Killer Sudoku |
|---|---|---|
| Starting clues | Pre-filled digits (17–45) | Usually none — only cage sums |
| Cage constraint | None | Sum + no repeat inside cage |
| Math required | None | Basic addition + combinations |
| Solving entry point | Scanning for singles | Locked cage combinations + 45-rule |
| Typical difficulty | Easy → Expert | Medium → Very Hard |
Killer Sudoku is a variant that combines classic Sudoku with arithmetic. The grid is divided into "cages" — irregular groups of cells outlined by dotted lines — each with a small sum printed in the corner. You must fill the grid following all standard Sudoku rules, and additionally ensure that the digits in each cage add up to the cage's sum, with no digit repeating inside a cage.
Regular Sudoku gives you starting digits (clues) and requires only row, column, and box uniqueness. Killer Sudoku has very few or no starting digits — instead, you are given cage sums. The cage constraints replace clues as the entry point for solving. This makes Killer Sudoku rely more on arithmetic combinations than pure visual scanning.
Three rules apply: (1) Each row, column, and 3×3 box must contain digits 1–9 exactly once. (2) The digits inside each cage must sum to the small number printed in its corner. (3) A digit cannot repeat within a single cage. The third rule is critical — it constrains which combinations of digits can fill a cage.
Most Killer Sudoku puzzles have no starting digits at all — the cage sums alone determine the unique solution. Some easier Killer variants do include a few starting digits, but the pure form is sum-only. This is what makes Killer puzzles so satisfying: a fully empty grid still yields one unique solution through logic alone.
Start with cage sums that have only one possible combination. A 2-cell cage summing to 3 must be {1,2}. A 3-cell cage summing to 6 must be {1,2,3}. A 2-cell cage summing to 17 must be {8,9}. These "locked" cages give you a strong starting point. Combine cage logic with regular Sudoku scanning to progress through the puzzle.
Each row, column, and box must total 45 (1+2+...+9). If cages within a unit nearly cover it but leave one cell unaccounted for ("innie") or extend one cell outside ("outie"), you can calculate that extra cell's value by subtraction. Innies and outies are uniquely powerful in Killer Sudoku and not available in classic Sudoku.
Killer Sudoku is typically harder for beginners because it adds an arithmetic layer on top of standard Sudoku logic. However, the cage sums also provide more constraints than typical clues, so once you learn the technique it can sometimes be easier than expert-level standard Sudoku. Experienced solvers often prefer Killer for its variety.
You need basic addition and the ability to enumerate small combinations of digits 1–9. You do not need advanced math. Most experienced Killer solvers memorize common cage combinations (e.g., 2-cell sum of 17 = {8,9}) so the arithmetic becomes pattern recognition rather than calculation.