Kakuro
How to solve Kakuro: the sums that have only one answer
Updated Tuesday, October 27
To solve a Kakuro, start with the runs whose total can only be made one way, then look at the squares where an across run and a down run cross: the digit must suit both. Every Gridarium kakuro can be finished this way, without guessing.
The rules
Fill each white square with a digit from 1 to 9. White squares form runs, across and down. The number above the diagonal of a black square is the total of the run to its right; the number below is the total of the run underneath. A digit never repeats inside a run.
Step 1: runs with only one answer
Some totals can only be made with one set of different digits. Spot these first: the digits are known, only their order is left.
| Run | Total | Digits |
|---|---|---|
| 2 squares | 3 | 1 + 2 |
| 2 squares | 4 | 1 + 3 |
| 2 squares | 16 | 7 + 9 |
| 2 squares | 17 | 8 + 9 |
| 3 squares | 6 | 1 + 2 + 3 |
| 3 squares | 7 | 1 + 2 + 4 |
| 3 squares | 23 | 6 + 8 + 9 |
| 3 squares | 24 | 7 + 8 + 9 |
| 4 squares | 10 | 1 + 2 + 3 + 4 |
| 4 squares | 11 | 1 + 2 + 3 + 5 |
| 4 squares | 29 | 5 + 7 + 8 + 9 |
| 4 squares | 30 | 6 + 7 + 8 + 9 |
| 5 squares | 15 | 1 + 2 + 3 + 4 + 5 |
| 5 squares | 16 | 1 + 2 + 3 + 4 + 6 |
| 5 squares | 34 | 4 + 6 + 7 + 8 + 9 |
| 5 squares | 35 | 5 + 6 + 7 + 8 + 9 |
Step 2: where two runs cross
Every white square sits in one across run and one down run. Its digit must fit both. A two-square run of 4 (1 and 3) crossing a two-square run of 16 (7 and 9) has no digit in common: look elsewhere. A run of 3 (1 and 2) crossing a run of 4 (1 and 3) can only share the 1.
Step 3: count the ways
Most totals have a few ways. Three squares adding up to 12 can be 1 + 2 + 9, 1 + 3 + 8, 1 + 4 + 7, 1 + 5 + 6, 2 + 3 + 7, 2 + 4 + 6, 3 + 4 + 5: 7 sets. Write the possible digits as notes and cross them out as the crossing runs fill in. The Run sums button lists the sets for you.
Step 4: the totals of a whole block
On big grids, add up the clues of a block of rows that the runs cover completely, and compare with the clues of the columns that cross it: the difference is what the squares sticking out must hold. Hard puzzles sometimes need this.
The three levels
- Easy: 5 by 5 squares, runs of up to 4.
- Medium: 7 by 7 squares, runs of up to 5.
- Hard: 9 by 9 squares, runs of up to 7.