Kakuro
Kakuro Sum 23 — All 3-Cell Combinations
Updated June 10, 2026 · 2 min read
A 3-cell Kakuro run with a clue of 23 has 1 valid combination. Each cell must contain a unique digit from 1 to 9, no repeats.
Forced combination. A 3-cell run summing to 23 can only use digits 6, 8, 9. Both values are fixed — only their order within the run remains.
Valid combinations
| Digits (any order) | Sum |
|---|
| 6 + 8 + 9 | = 23 |
What you know immediately
The digits 6, 8, 9 appear in every valid combination — certain in this run regardless of which combination applies.
Digits 1, 2, 3, 4, 5, 7 never appear in any valid combination — eliminate them immediately from all intersecting clues.
Why this clue is special
Twenty-three over three cells forces 6, 8 and 9 — note the missing 7, which would require the repeating 7+7+9 or 6+8+9's slot. As with all near-maximum clues, its power is in what it excludes: digits 1–5 and 7 are dead in all three cells, so any crossing run needing a small digit there is instantly constrained. 23-in-three crossing 6-in-three is a setter's classic: the shared cell must be the 6, the only digit in both sets.
Solving with this clue
- Cross out combinations made impossible by digits already placed in the run
- Find digits present in all remaining combinations — those are certain placements
- Find digits absent from all remaining combinations — remove from intersecting clues
- When one combination remains, all digits in the run are determined
Use intersections: A shared cell must satisfy both its row clue and column clue. Digits that don't appear in valid combinations for either clue are eliminated. This cross-elimination often reduces options to one quickly.
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