Kakuro pair
Two cells in a kakuro run sharing the same two-digit possible set. The two digits are confined to those two cells, eliminating them from every other cell of the run.
A kakuro pair is the kakuro analogue of the naked pair in Sudoku. Two cells in the same run have the same two-digit possible set — say {3, 7} — and no other cells in the run can contain those digits, because the two cells together must already account for them. Any other cell of the run can have 3 and 7 eliminated from its possible digits.
How a kakuro pair forms
Possible-digit sets for kakuro cells are produced by the cross-reference move — the intersection of the cell's horizontal run combinations and its vertical run combinations. When two cells in the same run produce the same two-digit set through cross-reference, a kakuro pair is alive.
A worked example. A 4-cell run with target 14. Two of its cells, through cross-reference with their other runs, both narrow to {2, 5}. The other two cells of the run have wider possible sets: {1, 2, 5, 6} and {1, 5, 6, 8}. The kakuro pair claims 2 and 5 for the first two cells. Remove 2 and 5 from the other two cells: the third becomes {1, 6} and the fourth becomes {1, 6, 8}. The run's combinations re-narrow accordingly, and the surrounding intersections feed back the new constraints.
Why "kakuro pair" rather than "naked pair"
The pattern is structurally identical to a Sudoku naked pair, but the kakuro version operates on runs rather than rows/columns/boxes, and the run's cell count and target sum interact with the pair's claim. A naked pair in Sudoku eliminates two digits from every other cell of the unit; a kakuro pair does the same for the run, and it constrains the run's remaining target sum (subtract the pair's two digits from the original target to get the sum the remaining cells must produce).
The dual constraint — eliminate the pair's digits and update the run's effective target — is what makes the move feel different in practice from its Sudoku cousin. After firing a kakuro pair, the player typically re-checks the run's possible combinations, since the new effective target may have shrunk the combination set further.
The kakuro-triple cousin
Kakuro triple is the three-cell version of the same pattern. Three cells in a run with the same three-digit possible set claim those three digits, eliminating them from the rest of the run and reducing the effective target accordingly. The reasoning generalises to four-cell quads and beyond, though larger versions are increasingly rare.
When you'll see it
Kakuro pairs appear regularly on medium-difficulty kakuros once the unique-sum and cross-reference passes have narrowed the cells. The signature is two cells whose cross-reference outputs are identical and small (typically {a, b} or {a, b, c} for a triple). Once you've seen a few, the pattern becomes part of the natural scan after every cross-reference update.
See also
- Naked pair— Two cells in the same unit whose candidate sets are identical and contain exactly two digits. Together they claim those digits across that unit and rule them out elsewhere.
- Run (kakuro)— A horizontal or vertical sum-segment in a kakuro grid. The white cells from one clue cell to the next, which must sum to the clue's target without repeating a digit.
- Cross-reference— Kakuro deduction at the intersection of two runs. The cell shared between a row run and a column run must hold a digit valid in both — usually pinning the cell directly.
- Kakuro triple— Three cells in a kakuro run sharing the same three-digit possible set — the kakuro analogue of the naked triple. Eliminates those digits from the rest of the run.
Read more
- Meet Kakuro
An introduction to Kakuro — what it is, how it differs from Sudoku, and why people who like number-logic puzzles often end up preferring it.