Killer Sudoku rules
Killer sudoku is sudoku with sums. The grid starts almost empty; what you have instead of digits are cages and their totals.
- Every row, column and 3x3 box contains the digits 1 to 9 once each.
- The digits in each dashed cage add up to the number in its corner.
- A digit never repeats inside a cage.
Killer sudoku is also called sum sudoku, and some puzzle books and apps print it as Sudoku Killer. If you already play sudoku online, killer is the variant to try next: the same grid, plus sums.
Try it on small grids
Three small Killer Sudoku puzzles to get the feel. Hints work here too and explain each step.
Practice 1 · 4x4 · Easy
Practice 2 · 4x4 · Easy
Practice 3 · 6x6 · Medium
Your first moves
Start with cages whose sum has only one combination: 3 in two cells is 1 and 2, 17 in two cells is 8 and 9, 24 in three cells is 7, 8 and 9. Pencil those digits in. Then find a row or box where the cages inside add up to almost 45: the missing amount is the cell (or the two cells) left over. Every digit you place also clears its row, column, box and cage.
A worked example, step by step
Our solver finished this Killer Sudoku (6x6) in 43 steps. Every step names its technique; step through it on the board, or read the whole solve below.
All 43 steps
- Cage combinations. The cage of 14 in 3 cells (D1, C2, D2) can only be 3+5+6 with the candidates left, so D1, C2, D2 lose the other digits.
- Cage combinations. The cage of 3 in 2 cells (E1, E2) can only be 1+2 with the candidates left, so E1, E2 lose the other digits.
- Cage combinations. The cage of 3 in 1 cell (F1) can only be 3 with the candidates left, so F1 loses the other digits.
- Naked single. F1 can only be 3, so 3 is ruled out for the other cells of its row, column, box and cage.
- Hidden single. In box 2, only F2 can take 4.
- Naked single. F2 can only be 4, so 4 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 10 in 3 cells (A1, B1, C1) can only be 1+4+5 with the candidates left, so A1, B1, C1 lose the other digits.
- Hidden single. In row 1, only E1 can take 2.
- Naked single. E1 can only be 2, so 2 is ruled out for the other cells of its row, column, box and cage.
- Naked single. E2 can only be 1, so 1 is ruled out for the other cells of its row, column, box and cage.
- Hidden single. In row 1, only D1 can take 6.
- Naked single. D1 can only be 6, so 6 is ruled out for the other cells of its row, column, box and cage.
- Naked single. D2 can only be 5, so 5 is ruled out for the other cells of its row, column, box and cage.
- Naked single. C2 can only be 3, so 3 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 12 in 3 cells (A2, B2, A3) can only be 2+4+6 with the candidates left, so A3 loses the other digits.
- Naked single. A3 can only be 4, so 4 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 15 in 4 cells (F2, D3, E3, F3) can only be 2+3+4+6 with the candidates left, so D3, E3, F3 lose the other digits.
- Cage combinations. The cage of 4 in 2 cells (B3, B4) can only be 1+3 with the candidates left, so B3, B4 lose the other digits.
- Hidden single. In row 3, only C3 can take 5.
- Naked single. C3 can only be 5, so 5 is ruled out for the other cells of its row, column, box and cage.
- Hidden single. In row 3, only B3 can take 1.
- Naked single. B3 can only be 1, so 1 is ruled out for the other cells of its row, column, box and cage.
- Naked single. B4 can only be 3, so 3 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 7 in 2 cells (C3, C4) can only be 2+5 with the candidates left, so C4 loses the other digits.
- Naked single. C4 can only be 2, so 2 is ruled out for the other cells of its row, column, box and cage.
- Naked single. A4 can only be 6, so 6 is ruled out for the other cells of its row, column, box and cage.
- Naked single. A2 can only be 2, so 2 is ruled out for the other cells of its row, column, box and cage.
- Naked single. B2 can only be 6, so 6 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 14 in 3 cells (A4, A5, B5) can only be 3+5+6 with the candidates left, so A5, B5 lose the other digits.
- Naked single. A5 can only be 3, so 3 is ruled out for the other cells of its row, column, box and cage.
- Naked single. B5 can only be 5, so 5 is ruled out for the other cells of its row, column, box and cage.
- Naked single. B1 can only be 4, so 4 is ruled out for the other cells of its row, column, box and cage.
- Naked single. C1 can only be 1, so 1 is ruled out for the other cells of its row, column, box and cage.
- Naked single. A6 can only be 1, so 1 is ruled out for the other cells of its row, column, box and cage.
- Naked single. B6 can only be 2, so 2 is ruled out for the other cells of its row, column, box and cage.
- Cage combinations. The cage of 16 in 4 cells (D4, E4, F4, E5) can only be 1+4+5+6 with the candidates left, so E5 loses the other digits.
- Naked single. E5 can only be 6, so 6 is ruled out for the other cells of its row, column, box and cage.
- Naked single. E3 can only be 3, so 3 is ruled out for the other cells of its row, column, box and cage.
- Naked single. D3 can only be 2, so 2 is ruled out for the other cells of its row, column, box and cage.
- Naked single. C5 can only be 4, so 4 is ruled out for the other cells of its row, column, box and cage.
- Naked single. D5 can only be 1, so 1 is ruled out for the other cells of its row, column, box and cage.
- Naked single. D4 can only be 4, so 4 is ruled out for the other cells of its row, column, box and cage.
- Naked single. E4 can only be 5, so 5 is ruled out for the other cells of its row, column, box and cage.
Common mistakes
- Forgetting that a cage cannot repeat a digit, even when the cage spans two boxes.
- Applying the rule of 45 with a cage that only partly lies in the house: count only whole cages, then deal with the parts.
- Ignoring the sudoku rules in favour of the sums: most placements still come from singles.
Where Killer Sudoku comes from
Killer sudoku grew up next to classic sudoku in Japanese puzzle magazines and became a newspaper favourite in the mid-2000s. It keeps every sudoku rule and adds arithmetic, which is why it often has no given digits at all.