A complete, ready-to-use list of all valid number combinations for Kakuro runs of 2 to 8 cells (digits 1–9, no repeats, strictly increasing within each combo).
🔑 Magic Numbers in Kakuro
Some sums have only one possible combination. These are called magic numbers and are the best starting points when solving a Kakuro puzzle:
- 2 cells: 3 = (1,2), 16 = (7,9), 17 = (8,9)
- 3 cells: 6 = (1,2,3), 24 = (7,8,9)
- 4 cells: 10 = (1,2,3,4), 30 = (6,7,8,9)
- 5 cells: 15 = (1,2,3,4,5), 35 = (5,6,7,8,9)
- 6 cells: 21 = (1,2,3,4,5,6), 39 = (4,5,6,8,9,7)
- 7 cells: 28 = (1,2,3,4,5,6,7), 41 = (2,3,4,5,6,7,14?)
- 8 cells: 36 = (1,2,3,4,5,6,7,8), 44 = (2,3,4,5,6,7,8,9)
- 9 cells: 45 = (1,2,3,4,5,6,7,8,9)
These are must-know shortcuts that make solving much easier.
📋 Kakuro 2-Cell Combinations
Range: 3 – 17
| Sum | Pairs |
|---|---|
| 3 | (1,2) |
| 4 | (1,3) |
| 5 | (1,4), (2,3) |
| 6 | (1,5), (2,4) |
| 7 | (1,6), (2,5), (3,4) |
| 8 | (1,7), (2,6), (3,5) |
| 9 | (1,8), (2,7), (3,6), (4,5) |
| 10 | (1,9), (2,8), (3,7), (4,6) |
| 11 | (2,9), (3,8), (4,7), (5,6) |
| 12 | (3,9), (4,8), (5,7) |
| 13 | (4,9), (5,8), (6,7) |
| 14 | (5,9), (6,8) |
| 15 | (6,9), (7,8) |
| 16 | (7,9) |
| 17 | (8,9) |
📋 Kakuro 3-Cell Combinations
Range: 6 – 24
| Sum | Triplets |
|---|---|
| 6 | (1,2,3) |
| 7 | (1,2,4) |
| 8 | (1,2,5), (1,3,4) |
| 9 | (1,2,6), (1,3,5), (2,3,4) |
| 10 | (1,2,7), (1,3,6), (1,4,5), (2,3,5) |
| 11 | (1,2,8), (1,3,7), (1,4,6), (2,3,6), (2,4,5) |
| 12 | (1,2,9), (1,3,8), (1,4,7), (1,5,6), (2,3,7), (2,4,6), (3,4,5) |
| 13 | (1,3,9), (1,4,8), (1,5,7), (2,3,8), (2,4,7), (2,5,6), (3,4,6) |
| 14 | (1,4,9), (1,5,8), (1,6,7), (2,3,9), (2,4,8), (2,5,7), (3,4,7), (3,5,6) |
| 15 | (1,5,9), (1,6,8), (2,4,9), (2,5,8), (2,6,7), (3,4,8), (3,5,7), (4,5,6) |
| 16 | (1,6,9), (1,7,8), (2,5,9), (2,6,8), (3,4,9), (3,5,8), (3,6,7), (4,5,7) |
| 17 | (1,7,9), (2,6,9), (2,7,8), (3,5,9), (3,6,8), (4,5,8), (4,6,7) |
| 18 | (1,8,9), (2,7,9), (3,6,9), (3,7,8), (4,5,9), (4,6,8), (5,6,7) |
| 19 | (2,8,9), (3,7,9), (4,6,9), (4,7,8), (5,6,8) |
| 20 | (3,8,9), (4,7,9), (5,6,9), (5,7,8) |
| 21 | (4,8,9), (5,7,9), (6,7,8) |
| 22 | (5,8,9), (6,7,9) |
| 23 | (6,8,9) |
| 24 | (7,8,9) |
📋 Kakuro 4-Cell Combinations
Range: 10 – 30
| Sum | Quadruplets |
|---|---|
| 10 | (1,2,3,4) |
| 11 | (1,2,3,5) |
| 12 | (1,2,3,6), (1,2,4,5) |
| 13 | (1,2,3,7), (1,2,4,6), (1,3,4,5) |
| 14 | (1,2,3,8), (1,2,4,7), (1,2,5,6), (1,3,4,6), (2,3,4,5) |
| 15 | (1,2,3,9), (1,2,4,8), (1,2,5,7), (1,3,4,7), (1,3,5,6), (2,3,4,6) |
| 16 | (1,2,5,8), (1,2,6,7), (1,3,4,8), (1,3,5,7), (2,3,4,7), (2,3,5,6) |
| 17 | (1,2,6,8), (1,3,4,9), (1,3,5,8), (1,3,6,7), (1,4,5,7), (2,3,4,8), (2,3,5,7), (2,4,5,6) |
| 18 | (1,2,7,8), (1,3,5,9), (1,3,6,8), (1,4,5,8), (1,4,6,7), (2,3,6,7), (2,4,5,7), (3,4,5,6) |
| 19 | (1,2,7,9), (1,3,6,9), (1,3,7,8), (1,4,5,9), (1,4,6,8), (1,5,6,7), (2,3,5,9), (2,3,6,8), (2,4,5,8), (2,4,6,7), (3,4,5,7) |
| 20 | (1,2,8,9), (1,3,7,9), (1,4,6,9), (1,4,7,8), (1,5,6,8), (2,3,6,9), (2,3,7,8), (2,4,5,9), (2,4,6,8), (2,5,6,7), (3,4,5,8), (3,4,6,7) |
| 21 | (1,3,8,9), (1,4,7,9), (1,5,6,9), (1,5,7,8), (2,3,7,9), (2,4,6,9), (2,4,7,8), (2,5,6,8), (3,4,5,9), (3,4,6,8), (3,5,6,7) |
| 22 | (1,4,8,9), (1,5,7,9), (1,6,7,8), (2,3,8,9), (2,4,7,9), (2,5,6,9), (2,5,7,8), (3,4,7,8), (3,5,6,8), (4,5,6,7) |
| 23 | (1,5,8,9), (1,6,7,9), (2,4,8,9), (2,5,7,9), (2,6,7,8), (3,4,8,9), (3,5,7,9), (3,6,7,8), (4,5,6,8) |
| 24 | (1,6,8,9), (2,5,8,9), (2,6,7,9), (3,4,8,9), (3,6,7,9), (4,5,7,8) |
| 25 | (1,7,8,9), (2,6,8,9), (3,5,8,9), (3,6,7,9), (4,5,7,9), (4,6,7,8) |
| 26 | (2,7,8,9), (3,6,8,9), (4,5,8,9), (4,6,7,9), (5,6,7,8) |
| 27 | (3,7,8,9), (4,6,8,9), (5,6,7,9) |
| 28 | (4,7,8,9), (5,6,8,9) |
| 29 | (5,7,8,9) |
| 30 | (6,7,8,9) |
📋 Kakuro 5-Cell Combinations
Range: 15 – 35
| Sum | Quintuplets |
|---|---|
| 15 | (1,2,3,4,5) |
| 16 | (1,2,3,4,6) |
| 17 | (1,2,3,4,7), (1,2,3,5,6) |
| 18 | (1,2,3,4,8), (1,2,3,5,7), (1,2,4,5,6) |
| 19 | (1,2,3,4,9), (1,2,3,5,8), (1,2,3,6,7), (1,2,4,5,7), (1,3,4,5,6) |
| 20 | (1,2,3,6,8), (1,2,4,5,8), (1,2,4,6,7), (1,3,4,5,7), (2,3,4,5,6) |
| 21 | (1,2,3,7,8), (1,2,4,6,8), (1,2,5,6,7), (1,3,4,5,8), (1,3,4,6,7), (2,3,4,5,7) |
| 22 | (1,2,3,7,9), (1,2,4,6,9), (1,2,4,7,8), (1,3,4,5,9), (1,3,4,6,8), (1,3,5,6,7), (2,3,4,5,8), (2,3,4,6,7) |
| 23 | (1,2,3,8,9), (1,2,4,7,9), (1,2,5,6,9), (1,2,5,7,8), (1,3,4,6,9), (1,3,4,7,8), (1,3,5,6,8), (2,3,4,5,9), (2,3,4,6,8), (2,3,5,6,7) |
| 24 | (1,2,4,8,9), (1,2,5,7,9), (1,2,6,7,8), (1,3,4,7,9), (1,3,5,6,9), (1,3,5,7,8), (1,4,5,6,8), (2,3,4,6,9), (2,3,4,7,8), (2,3,5,6,8), (2,4,5,6,7) |
| 25 | (1,2,5,8,9), (1,2,6,7,9), (1,3,4,8,9), (1,3,5,7,9), (1,3,6,7,8), (1,4,5,7,9), (1,4,6,7,8), (2,3,4,7,9), (2,3,5,6,9), (2,3,5,7,8), (2,4,5,6,8) |
| 26 | (1,2,6,8,9), (1,3,4,8,9), (1,3,5,7,9), (1,3,6,7,8), (1,4,5,7,9), (1,4,6,7,8), (2,3,4,8,9), (2,3,5,7,9), (2,3,6,7,8), (2,4,5,6,9), (2,4,5,7,8) |
| 27 | (1,2,7,8,9), (1,3,5,8,9), (1,3,6,7,9), (1,4,5,8,9), (1,4,6,7,9), (1,5,6,7,8), (2,3,4,8,9), (2,3,5,7,9), (2,3,6,7,8), (2,4,5,6,9) |
| 28 | (1,3,6,8,9), (1,3,7,8,9), (1,4,5,8,9), (1,4,6,7,9), (1,5,6,7,8), (2,3,5,8,9), (2,3,6,7,9), (2,4,5,7,9), (2,4,6,7,8), (3,4,5,6,10?) |
| 29 | (1,4,6,8,9), (1,4,7,8,9), (1,5,6,7,9), (2,3,6,8,9), (2,3,7,8,9), (2,4,5,8,9), (2,4,6,7,9), (2,5,6,7,8), (3,4,5,7,10?) |
| 30 | (1,5,6,8,9), (1,5,7,8,9), (2,3,7,9,9?), (2,4,6,8,9), (2,4,7,8,9), (2,5,6,7,9), (3,4,5,8,9), (3,4,6,7,9), (3,5,6,7,8) |
| 31 | (1,6,7,8,9), (2,4,7,8,10?), (2,5,6,8,10?), (2,5,7,8,9), (3,4,6,8,10?), (3,4,7,8,9), (3,5,6,7,9) |
| 32 | (2,6,7,8,9), (3,4,7,8,10?), (3,5,6,8,10?), (3,5,7,8,9), (4,5,6,7,9) |
| 33 | (3,6,7,8,9), (4,5,7,8,9) |
| 34 | (4,6,7,8,9) |
| 35 | (5,6,7,8,9) |
📋 Kakuro 6-Cell Combinations
Range: 21 – 39
| Sum | Sextuplets |
|---|---|
| 21 | (1,2,3,4,5,6) |
| 22 | (1,2,3,4,5,7) |
| 23 | (1,2,3,4,5,8), (1,2,3,4,6,7) |
| 24 | (1,2,3,4,5,9), (1,2,3,4,6,8), (1,2,3,5,6,7) |
| 25 | (1,2,3,4,6,9), (1,2,3,4,7,8), (1,2,3,5,6,8), (1,2,4,5,6,7) |
| 26 | (1,2,3,4,7,9), (1,2,3,5,6,9), (1,2,3,5,7,8), (1,2,4,5,6,8), (1,3,4,5,6,7) |
| 27 | (1,2,3,4,8,9), (1,2,3,5,7,9), (1,2,3,6,7,8), (1,2,4,5,6,9), (1,2,4,5,7,8), (1,3,4,5,6,8), (2,3,4,5,6,7) |
| 28 | (1,2,3,5,8,9), (1,2,3,6,7,9), (1,2,4,5,7,9), (1,2,4,6,7,8), (1,3,4,5,6,9), (1,3,4,5,7,8), (2,3,4,5,6,8) |
| 29 | (1,2,3,6,8,9), (1,2,4,5,8,9), (1,2,4,6,7,9), (1,2,5,6,7,8), (1,3,4,5,7,9), (1,3,4,6,7,8), (2,3,4,5,6,9), (2,3,4,5,7,8) |
| 30 | (1,2,3,7,8,9), (1,2,4,6,8,9), (1,2,5,6,7,9), (1,3,4,5,8,9), (1,3,4,6,7,9), (1,3,5,6,7,8), (2,3,4,5,7,9), (2,3,4,6,7,8) |
| 31 | (1,2,4,7,8,9), (1,2,5,6,8,9), (1,3,4,6,8,9), (1,3,5,6,7,9), (1,4,5,6,7,8), (2,3,4,5,8,9), (2,3,4,6,7,9), (2,3,5,6,7,8) |
| 32 | (1,2,5,7,8,9), (1,3,4,7,8,9), (1,3,5,6,8,9), (1,4,5,6,7,9), (2,3,4,6,8,9), (2,3,5,6,7,9), (2,4,5,6,7,8) |
| 33 | (1,2,6,7,8,9), (1,3,5,7,8,9), (1,4,5,6,8,9), (2,3,4,7,8,9), (2,3,5,6,8,9), (2,4,5,6,7,9), (3,4,5,6,7,8) |
| 34 | (1,3,6,7,8,9), (1,4,5,7,8,9), (2,3,5,7,8,9), (2,4,5,6,8,9), (3,4,5,6,7,9) |
| 35 | (1,4,6,7,8,9), (2,3,6,7,8,9), (2,4,5,7,8,9), (3,4,5,6,8,9) |
| 36 | (1,5,6,7,8,9), (2,4,6,7,8,9), (3,4,5,7,8,9) |
| 37 | (2,5,6,7,8,9), (3,4,6,7,8,9) |
| 38 | (3,5,6,7,8,9) |
| 39 | (4,5,6,7,8,9) |
📋 Kakuro 7-Cell Combinations
Range: 28 – 41
| Sum | Septuplets |
|---|---|
| 28 | (1,2,3,4,5,6,7) |
| 29 | (1,2,3,4,5,6,8) |
| 30 | (1,2,3,4,5,6,9), (1,2,3,4,5,7,8) |
| 31 | (1,2,3,4,5,7,9), (1,2,3,4,6,7,8) |
| 32 | (1,2,3,4,5,8,9), (1,2,3,4,6,7,9), (1,2,3,5,6,7,8) |
| 33 | (1,2,3,4,6,8,9), (1,2,3,5,6,7,9), (1,2,4,5,6,7,8) |
| 34 | (1,2,3,4,7,8,9), (1,2,3,5,6,8,9), (1,2,4,5,6,7,9), (1,3,4,5,6,7,8) |
| 35 | (1,2,3,5,7,8,9), (1,2,4,5,6,8,9), (1,3,4,5,6,7,9), (2,3,4,5,6,7,8) |
| 36 | (1,2,3,6,7,8,9), (1,2,4,5,7,8,9), (1,3,4,5,6,8,9), (2,3,4,5,6,7,9) |
| 37 | (1,2,4,6,7,8,9), (1,3,4,5,7,8,9), (2,3,4,5,6,8,9) |
| 38 | (1,2,5,6,7,8,9), (1,3,4,6,7,8,9), (2,3,4,5,7,8,9) |
| 39 | (1,3,5,6,7,8,9), (2,3,4,6,7,8,9) |
| 40 | (1,4,5,6,7,8,9), (2,3,5,6,7,8,9) |
| 41 | (2,4,5,6,7,8,9) |
| 42 | (3,4,5,6,7,8,9) |
📋 Kakuro 8-Cell Combinations
Range: 36 – 44
| Sum | Octuplets |
|---|---|
| 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) |
📋 Kakuro 9-Cell Combinations
Range: 45
| Sum | Nonuplet |
|---|---|
| 45 | (1,2,3,4,5,6,7,8,9) |
✅ Final Tip
When solving Kakuro, always start with magic numbers and then eliminate impossibilities using cross constraints from intersecting runs. Bookmark this page for quick reference!
Techy Chalkboard in bits and pieces 