Killer Sudoku
Killer Sudoku combines the pure logic of classic Sudoku with the challenge of arithmetic. Digits in cages must sum to the cage total, and no digit may repeat within a cage.
How is Killer Sudoku Different?
In Killer Sudoku, cells are grouped into coloured cages shown with dashed borders. Each cage displays a target sum in its top-left corner. Every digit inside a cage must add up to that sum - And no digit can repeat within a cage, even though cages can span multiple rows, columns, and boxes.
The standard Sudoku rules still apply: each digit 1–9 must appear exactly once in every row, column, and 3×3 box. Killer Sudoku simply adds the cage constraint on top of them.
Key differences at a glance
| Classic Sudoku | Killer Sudoku | |
|---|---|---|
| Given numbers | Yes - Pre-filled clues | No - Cage sums are the only clues |
| Extra constraint | None | Cage sums (digits in cage must add to target) |
| Digit repeats in cage | N/A | Not allowed |
| Arithmetic required | No | Yes - Basic addition |
| Techniques needed | Singles, Pairs | Same + cage elimination |
How to read cages
- Find a cage (a group of cells outlined with dashes).
- Look at its sum clue in the top-left cell of the cage.
- Determine which combination of unique digits could produce that sum - For example, a 2-cell cage summing to 3 must be {1, 2}.
- Apply the standard row/column/box rules to narrow down which digit goes where.
- Use pencil marks to track remaining possibilities.
Useful cage sum facts
| Cage size | Min possible sum | Max possible sum | Example combos |
|---|---|---|---|
| 2 cells | 3 (1+2) | 17 (8+9) | Sum 4 → {1,3} |
| 3 cells | 6 (1+2+3) | 24 (7+8+9) | Sum 6 → {1,2,3} |
| 4 cells | 10 (1+2+3+4) | 30 (6+7+8+9) | Sum 10 → {1,2,3,4} |
| 9 cells (full unit) | Always 45 | 1+2+…+9 = 45 | |
Tip: The sum of all nine cells in any row, column, or box is always 45. Use this to figure out the value of unlabelled cells when you know all other cage sums in a unit - It's one of the most powerful Killer Sudoku shortcuts.