How to solve Kakuro
Kakuro is a crossword made of sums. Every puzzle here has exactly one solution, and you can reach it by logic alone. These four ideas carry you through most grids, and the worked example below uses them all.
The rules in one minute
- Fill every white cell with a digit from 1 to 9.
- Each run of white cells, across or down, must add up to its clue. The number in the top-right half of a dark cell is the total for the white cells to its right; the number in the bottom-left half is the total for the white cells below it.
- No digit may repeat within a run. The same digit can appear again in a different run.
1. Learn the sums with only one combination
Most totals can be made several ways, but some can be made only one way. A 3 in two cells is always 1 and 2, in some order; a 24 in three cells is always 7, 8 and 9. Spotting these gives you exact digits to work with straight away.
| Cells | Total | The only digits |
|---|---|---|
| 2 | 3 | 1 + 2 |
| 2 | 4 | 1 + 3 |
| 2 | 16 | 7 + 9 |
| 2 | 17 | 8 + 9 |
| 3 | 6 | 1 + 2 + 3 |
| 3 | 7 | 1 + 2 + 4 |
| 3 | 23 | 6 + 8 + 9 |
| 3 | 24 | 7 + 8 + 9 |
| 4 | 10 | 1 + 2 + 3 + 4 |
| 4 | 11 | 1 + 2 + 3 + 5 |
| 4 | 29 | 5 + 7 + 8 + 9 |
| 4 | 30 | 6 + 7 + 8 + 9 |
2. Use the no-repeat rule
Because a run can't repeat a digit, a two-cell 8 can't be 4 and 4, so it must be 1 and 7, 2 and 6, or 3 and 5. Once a digit is placed in a run, cross it off for the run's other cells, and drop any combination that would need it twice.
3. Cross the runs
Every white cell belongs to one across run and one down run, and its digit must fit both. List what each run allows and keep only the digits in both lists. Cells where two tight runs cross often have a single digit left.
4. Finish a run from its total
When a run has one empty cell left, that cell is the clue minus the digits already placed. Every finished run then narrows the runs that cross it, so a good solve is a chain of small, certain steps.
A worked example
Here is a small grid with ten white cells. Each picture shows the digits written so far, with the newest ones highlighted.
The empty grid: four runs across and four runs down.
1. Start in the top-left corner. The across 3 and the down 4 each cover two cells. 3 can only be 1 + 2 and 4 can only be 1 + 3, so the cell where they meet must hold the digit they share: 1.
2. Each of those runs now has one cell left. The across 3 needs a 2 next to the 1, and the down 4 needs a 3 below it.
3. Look at the cell where the across 18 meets the down 10. The across 18 already has a 3, so its other two cells make 15: 6 + 9 or 7 + 8. The down 10 already has a 2, so its other two cells make 8: 1 + 7 or 3 + 5. The only digit in both lists is 7.
4. Finish both runs: the across 18 needs an 8 in its last cell (18 − 3 − 7), and the down 10 needs a 1 (10 − 2 − 7).
5. Now the bottom-right corner. In two cells, 16 can only be 7 + 9 and 17 can only be 8 + 9. Where the across 16 and the down 17 meet, the shared digit is 9.
6. That leaves a 7 to finish the across 16 and an 8 to finish the down 17.
7. One white cell is left, in the middle of the across 14, which already has 1 and 8: so it is 5. Check it against the down 20: 8 + 5 + 7 = 20. Solved.
More tips
- Use Notes to pencil in the digits a cell could still be, and rub them out as runs fill up.
- A mistake is counted when you enter a digit that repeats in one of its runs, so check both runs before you type.
- Stuck? Look for the tightest crossing: two runs with few combinations meeting at one cell.
- Practise in Practice Mode or on past puzzles in the archive. Neither affects the leaderboard.