Kakuro
Kakuro Sum 4 — All 2-Cell Combinations
Updated June 10, 2026 · 2 min read
A 2-cell Kakuro run with a clue of 4 has 1 valid combination. Each cell must contain a unique digit from 1 to 9, no repeats.
Forced combination. A 2-cell run summing to 4 can only use digits 1, 3. Both values are fixed — only their order within the run remains.
Valid combinations
| Digits (any order) | Sum |
|---|
| 1 + 3 | = 4 |
What you know immediately
The digits 1, 3 appear in every valid combination — certain in this run regardless of which combination applies.
Digits 2, 4, 5, 6, 7, 8, 9 never appear in any valid combination — eliminate them immediately from all intersecting clues.
Why this clue is special
A clue of 4 over two cells is a magic clue: only 1 and 3 work, since 2+2 would repeat a digit and repeats are illegal inside a run. That repeat rule is exactly what makes even sums over two cells stronger than they look — half of their arithmetic options vanish. When a sum-4 run crosses a sum-3 run, the shared cell must be the 1 if it's the only digit the two combination sets have in common; check the intersection before writing anything.
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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