Home / How to play Kakuro
How to play Kakuro
Updated 15 October 2026
Kakuro is a crossword made of numbers. The rules take a minute to learn, and a handful of techniques will take you through most puzzles without a single guess.
The rules
- Fill every white square with a digit from 1 to 9.
- A run is a line of white squares across or down, bounded by dark squares or the edge of the grid.
- The clue at the start of each run gives its total. The number in the top-right of a clue square is for the run going across; the bottom-left number is for the run going down.
- Digits in a run must all be different. You can't make 4 with 2 + 2.
Like Sudoku, a proper Kakuro has exactly one solution and can be solved by logic alone.
Technique 1: learn the unique sums
Some totals can only be made one way, and they're the best place to start. The most useful ones:
| Squares | Low total | Must be | High total | Must be |
|---|---|---|---|---|
| 2 | 3 | 1 2 | 17 | 8 9 |
| 2 | 4 | 1 3 | 16 | 7 9 |
| 3 | 6 | 1 2 3 | 24 | 7 8 9 |
| 3 | 7 | 1 2 4 | 23 | 6 8 9 |
| 4 | 10 | 1 2 3 4 | 30 | 6 7 8 9 |
| 4 | 11 | 1 2 3 5 | 29 | 5 7 8 9 |
| 5 | 15 | 1 2 3 4 5 | 35 | 5 6 7 8 9 |
The full list for every length is on the Kakuro combinations chart.
Technique 2: where two runs cross
Every white square sits in one across run and one down run, and its digit must fit both. Suppose a square is in an across run of 3 in two squares (so it's 1 or 2) and a down run of 16 in two squares (so it's 7 or 9). No digit fits both, so the grid must be wrong. More usefully: if the down run were 4 in two squares (1 or 3), the only digit that fits both is 1.
Technique 3: high and low limits
Even when a total has several combinations, some digits are impossible. Two squares totalling 10 can be 1+9, 2+8, 3+7 or 4+6, so every digit except 5 is possible (5 would need a second 5). Three squares totalling 22 can only be 9+8+5 or 9+7+6, so the run must contain a 9, and no digit can be smaller than 5. The two largest digits, 9 and 8, only make 17, so the third has to be at least 5.
Technique 4: the last square in a run
Once every square in a run but one is filled, the last digit is simply the total minus the others. This is how most grids finish: one placed digit sets off a chain of forced squares.
A worked example
Take a square where an across run of 4 in two squares crosses a down run of 3 in two squares. The across run must be 1 and 3; the down run must be 1 and 2. The only digit in both is 1, so the shared square is 1. That makes the rest of the across run 3, and the rest of the down run 2, and each of those digits then helps with the runs they sit in.
Tip: Start in the corners. Short runs with very low or very high totals almost always have a forced digit, and corners are where two short runs meet.
Where to go next
Keep the combinations chart open while you solve. If you're stuck on a puzzle from a book or newspaper, the Kakuro solver will show you the answer. For a different kind of challenge, try today's logic puzzle.