Killer sudoku rules and strategy
The rules
- Every row, column and 3×3 box contains the digits 1 to 9 exactly once, as in normal sudoku.
- The grid is divided into cages, shown with dashed lines. The small number in a cage is the sum of all digits in it.
- A digit cannot repeat inside a cage.
A killer sudoku usually starts with no digits at all. Every puzzle on this site has exactly one solution, so you never need to guess.
1. Start with cages that have one combination
Some sums can only be made one way. In two cells: 3 = 1+2, 4 = 1+3, 16 = 7+9, 17 = 8+9. In three cells: 6 = 1+2+3, 7 = 1+2+4, 23 = 6+8+9, 24 = 7+8+9. In four cells: 10 = 1+2+3+4, 11 = 1+2+3+5, 29 = 5+7+8+9, 30 = 6+7+8+9. You do not know the order yet, but you know which digits are there, and those digits cannot appear anywhere else in the same row, column or box if the cage sits inside it.
The full list for every cage size is in the combinations table.
2. Use the 45 rule
The digits 1 to 9 add up to 45. So every row, column and 3×3 box adds up to 45. If the cages inside one box add up to, say, 38 and only one square of the box is not covered by them, that square must be 45 − 38 = 7.
The same works for two or three rows or columns together: three full rows add up to 135, and two full boxes add up to 90.
3. Innies and outies
When cages stick out of a box, row or column, compare the sums. Squares of those cages that lie outside the area are called outies, and squares inside the area that are not covered by complete cages are innies. The difference between the cage sums and 45 tells you the sum of the outies, or of the innies. Often that is a small or large number with only one combination.
4. Combine cage and sudoku logic
A cage of 10 in two cells can be 1+9, 2+8, 3+7 or 4+6. If the row already has 1, 2 and 3 placed, it must be 4+6. Look for cages where the row, column or box rules out all but one combination.
5. Use notes
Write the possible digits as small notes. When two squares in a row can only be the same two digits, those digits are taken, and you can remove them from the rest of the row. The game removes a note automatically from the row, column, box and cage when you place that digit.
Levels on this site
- Easy: small cages, and a few single squares that give you a digit straight away.
- Medium: cages of up to four squares.
- Hard: bigger cages and no single squares.
- Expert: the largest cages and the fewest clues.
Ready? Play today’s killer sudoku or try classic sudoku first.