Killer Sudoku: rules, tips and the combinations chart

Killer Sudoku hides the digits and gives you sums instead. It's Sudoku with a little arithmetic, and once you know a handful of combinations it becomes one of the most satisfying ways to play.

The rules

1. The classic rule still holds: each row, column and 3×3 box contains 1 to 9 once.
2. The grid is covered by cages, drawn with dashed outlines. The small number in a cage's corner is the sum of its digits.
3. A digit never repeats inside a cage.

Most Killer puzzles start with an empty grid: the cage sums are the only clues.

Opening moves

1. Cages with only one combination

Some sums can only be made one way. A 2-cell cage of 3 must be 1 and 2; a 2-cell cage of 17 must be 8 and 9; a 3-cell cage of 6 must be 1, 2 and 3; a 3-cell cage of 24 must be 7, 8 and 9. You don't yet know which cell is which, but you know which digits are there, and that removes them from everything else in the same unit. The chart below marks every such cage.

2. The rule of 45

1 + 2 + … + 9 = 45, so every row, column and box sums to 45. If the cages wholly inside a box add up to 38, the one remaining cell must be 7. The same works across two or three rows: add the cages inside them and compare with 90 or 135.

3. Combine combinations with Sudoku

A 2-cell cage of 10 could be 1+9, 2+8, 3+7 or 4+6. If the row already has a 9 and an 8, the cage can't be 1+9 or 2+8. Narrow each cage's options, then pencil-mark as you would in classic Sudoku: naked pairs, pointing pairs and the rest all still apply.

Killer Sudoku combinations chart

Every set of different digits for each cage size and sum. Highlighted rows have only one possible combination. (A 9-cell cage always holds 1 to 9 and sums to 45.)

Killer in Ninebloom

Ninebloom's Killer puzzles come at Easy, Medium and Hard. Its hints count the cages: when you're stuck, a hint usually shows a cell whose digit is forced by its row, column, box and cage together, and says which of them rule the other digits out.