Solving guide
How to solve Killer Sudoku
Killer Sudoku looks daunting with no starting digits, but a handful of ideas does most of the work: cage combinations, the 45 rule and ordinary Sudoku logic.
The rules
Killer Sudoku follows the ordinary Sudoku rules: every row, column and 3×3 box contains 1 to 9 exactly once. But there are no starting digits. Instead the grid is divided into cages, drawn with dotted lines. The small number in each cage's corner is the total of its digits, and no digit may repeat within a cage.
1. Start with cages that have only one combination
Some totals can only be made one way. Two cells totalling 3 must be 1 and 2; two cells totalling 17 must be 8 and 9. You don't yet know which way round, but you know which digits, and that rules them out of the rest of the row, column or box whenever the cage sits inside one.
| Total | Must be |
|---|---|
| 3 | 1 + 2 |
| 4 | 1 + 3 |
| 16 | 7 + 9 |
| 17 | 8 + 9 |
| Total | Must be |
|---|---|
| 6 | 1 + 2 + 3 |
| 7 | 1 + 2 + 4 |
| 23 | 6 + 8 + 9 |
| 24 | 7 + 8 + 9 |
| Total | Must be |
|---|---|
| 10 | 1 + 2 + 3 + 4 |
| 11 | 1 + 2 + 3 + 5 |
| 29 | 5 + 7 + 8 + 9 |
| 30 | 6 + 7 + 8 + 9 |
Every total in these tables has exactly one possible set of digits. Learn the small and large ones first: they come up constantly.
2. The 45 rule
Every row, column and box adds up to 45 (1 + 2 + … + 9). So if you add the totals of the cages lying entirely inside a box, the cells left over must make up the difference. This is the single most useful idea in Killer Sudoku.
It works for rows and columns too, and for groups of them: two whole rows total 90, three total 135. When a cage pokes just one cell out of a box, the same arithmetic tells you that cell's value. Solvers call it an outie.
3. Combine with ordinary Sudoku
Once a few digits are pinned down, normal Sudoku techniques take over: singles, locked candidates and pairs, exactly as in our Sudoku guide. Cage maths and Sudoku logic feed each other. A digit placed in one cage narrows the options in the next.
4. Work out what a cage must contain
Even when a cage has several combinations, they often share a digit. A three-cell cage totalling 8 is either 1+2+5 or 1+3+4: either way it contains a 1. If that cage sits in one row, no other cell in the row can be 1.
How our levels differ
Easy Killer Sudoku uses cages of two or three cells and can be solved with combinations, the 45 rule and elimination. Medium puzzles add four-cell cages. Hard puzzles use cages of up to five cells, and you may need to test a two- or three-way choice to see which option holds up. Every puzzle has exactly one solution.