How to solve Killer Sudoku
Killer Sudoku is a Sudoku covered in cages: groups of squares outlined with a dotted line and a small sum in one corner. The digits in a cage add up to that sum and never repeat. Solve it with two tools on top of normal Sudoku: cage sums that allow only one set of digits, and the 45 rule.
The rules
- Every row, column and 3×3 box holds the digits 1 to 9 once, as in Sudoku.
- The digits in a cage add up to the cage's sum.
- No digit repeats inside a cage.
Most Killer Sudokus start with no digits at all. Everything comes from the cages.
Cages with only one answer
Some sums can be made in only one way. Two squares that add up to 3 must hold 1 and 2; two that add up to 17 must hold 8 and 9. You do not know the order yet, but you know the digits, and that is often enough to start. The full list, worked out by computer from every set of different digits from 1 to 9:
| Squares | Sums with only one answer (and the digits) |
|---|---|
| 2 | 3 (1+2), 4 (1+3), 16 (7+9), 17 (8+9) |
| 3 | 6 (1+2+3), 7 (1+2+4), 23 (6+8+9), 24 (7+8+9) |
| 4 | 10 (1+2+3+4), 11 (1+2+3+5), 29 (5+7+8+9), 30 (6+7+8+9) |
| 5 | 15 (1+2+3+4+5), 16 (1+2+3+4+6), 34 (4+6+7+8+9), 35 (5+6+7+8+9) |
| 6 | 21 (1+2+3+4+5+6), 22 (1+2+3+4+5+7), 38 (3+5+6+7+8+9), 39 (4+5+6+7+8+9) |
| 7 | 28 (1+2+3+4+5+6+7), 29 (1+2+3+4+5+6+8), 41 (2+4+5+6+7+8+9), 42 (3+4+5+6+7+8+9) |
| 8 | 36 (1+2+3+4+5+6+7+8), 37 (1+2+3+4+5+6+7+9), 38 (1+2+3+4+5+6+8+9), 39 (1+2+3+4+5+7+8+9), 40 (1+2+3+4+6+7+8+9), 41 (1+2+3+5+6+7+8+9), 42 (1+2+4+5+6+7+8+9), 43 (1+3+4+5+6+7+8+9), 44 (2+3+4+5+6+7+8+9) |
| 9 | 45 (1+2+3+4+5+6+7+8+9) |
Learn the two-square and three-square rows first; they come up all the time.
The 45 rule
The digits 1 to 9 add up to 45, so every row, column and box adds up to 45. If the cages inside a box cover all of it but one square, that square is 45 minus the cages.
Here three cages sit wholly inside the box and add up to 3, 17 and 20, which makes 40. The one square whose cage leaves the box must be 45 minus 40, which is 5. The same works across two or three boxes at once (a total of 90 or 135), and with a square that sticks out of a group of cages instead of one left over.
Tips
- Write the possible digit sets beside awkward cages, such as 15 in three squares, which can be made several ways.
- Look for 45-rule lines along each row and column, not only in boxes.
- Once a cage's digits are known, treat them like a naked pair or triple from normal Sudoku.
- Use every Sudoku technique as well: hidden singles still do much of the work late in a puzzle.
The same habit, in light
The 45 rule is counting what must be left over. Light Up has its own version: when a lantern would leave a neighbouring courtyard with nowhere to stand, that square is out. Nightwatch has a new Light Up board every night, free in your browser.
Nightwatch is on Android. On iPhone, play tonight's board here.
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Questions
How do you solve Killer Sudoku?
Start with cages whose sums allow only one set of digits, such as 3 in two squares (1 and 2) or 24 in three squares (7, 8 and 9). Then use the 45 rule: each row, column and box adds up to 45, so a square left over by the cages in a box is 45 minus their total. After that, normal Sudoku techniques take over.
What is the 45 rule in Killer Sudoku?
The digits 1 to 9 add up to 45, so every row, column and 3×3 box adds up to 45. When cages cover a box except for one square, that square equals 45 minus the sum of those cages.
Can digits repeat in a Killer Sudoku cage?
No. Digits never repeat inside a cage, even when the cage spans two boxes.