Locked (unique) combinations
These run lengths and sums can be made in exactly one way. The instant you see one, you know its digits, even before the order. They are the footholds every solve is built on.
| Cells | Sum | Only possible 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 |
| 5 | 15 | 1 2 3 4 5 |
| 5 | 16 | 1 2 3 4 6 |
| 5 | 34 | 4 6 7 8 9 |
| 5 | 35 | 5 6 7 8 9 |
| 6 | 21 | 1 2 3 4 5 6 |
| 6 | 22 | 1 2 3 4 5 7 |
| 6 | 38 | 3 5 6 7 8 9 |
| 6 | 39 | 4 5 6 7 8 9 |
| 7 | 28 | 1 2 3 4 5 6 7 |
| 7 | 29 | 1 2 3 4 5 6 8 |
| 7 | 41 | 2 4 5 6 7 8 9 |
| 7 | 42 | 3 4 5 6 7 8 9 |
| 8 | 36 | 1 2 3 4 5 6 7 8 |
| 8 | 37 | 1 2 3 4 5 6 7 9 |
| 8 | 38 | 1 2 3 4 5 6 8 9 |
| 8 | 39 | 1 2 3 4 5 7 8 9 |
| 8 | 40 | 1 2 3 4 6 7 8 9 |
| 8 | 41 | 1 2 3 5 6 7 8 9 |
| 8 | 42 | 1 2 4 5 6 7 8 9 |
| 8 | 43 | 1 3 4 5 6 7 8 9 |
| 8 | 44 | 2 3 4 5 6 7 8 9 |
Two-cell runs
Every possible sum for a run of two white cells, with all its combinations.
| Sum | Combinations |
|---|---|
| 3 | 12 |
| 4 | 13 |
| 5 | 14 23 |
| 6 | 15 24 |
| 7 | 16 25 34 |
| 8 | 17 26 35 |
| 9 | 18 27 36 45 |
| 10 | 19 28 37 46 |
| 11 | 29 38 47 56 |
| 12 | 39 48 57 |
| 13 | 49 58 67 |
| 14 | 59 68 |
| 15 | 69 78 |
| 16 | 79 |
| 17 | 89 |
Three-cell runs
The same for runs of three white cells. Note how the count peaks in the middle sums.
| Sum | Combinations |
|---|---|
| 6 | 123 |
| 7 | 124 |
| 8 | 125 134 |
| 9 | 126 135 234 |
| 10 | 127 136 145 235 |
| 11 | 128 137 146 236 245 |
| 12 | 129 138 147 156 237 246 345 |
| 13 | 139 148 157 238 247 256 346 |
| 14 | 149 158 167 239 248 257 347 356 |
| 15 | 159 168 249 258 267 348 357 456 |
| 16 | 169 178 259 268 349 358 367 457 |
| 17 | 179 269 278 359 368 458 467 |
| 18 | 189 279 369 378 459 468 567 |
| 19 | 289 379 469 478 568 |
| 20 | 389 479 569 578 |
| 21 | 489 579 678 |
| 22 | 589 679 |
| 23 | 689 |
| 24 | 789 |
Keep this page open in a second tab while you play a puzzle. The two-cell extremes (3, 4, 16, 17) and the three-cell extremes (6, 7, 23, 24) are the ones worth committing to memory first.
Frequently asked questions
What is a unique combination in Kakuro?+
A unique combination is a run length and sum that can be made in only one way. For example a two-cell run of 17 must be 8 and 9, and a three-cell run of 7 must be 1, 2 and 4. These are the most powerful clues because the digits are locked even before you know their order.
How many combinations are there for a sum?+
It depends on both the sum and the run length. A two-cell run of 10 has four combinations, while a two-cell run of 3 has only one. Shorter runs and extreme sums have the fewest combinations, which is why they are the best starting points.
Do I need to memorise the combination table?+
No. Experienced solvers remember the locked two and three-cell combinations because they appear constantly, but you can keep this reference open while you play. Over time the common ones stick.