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.
A kakuro triple is the three-cell extension of the kakuro pair. Three cells in the same run have a combined possible-digit set of exactly three digits — say {2, 5, 7}. The three cells together must hold those three digits in some arrangement; no other cell in the run can contain any of them. The eliminations fire on every other cell of the run, and the run's effective target shrinks by 2+5+7 = 14.
How a kakuro triple forms
The standard shape: three cells whose individual possible sets, produced by cross-reference, are some subset of the same three digits. Each cell might have only two of the three digits as its possible set, but the union across the three cells covers the full set. The classic shape is three cells with possible sets {2, 5}, {5, 7}, {2, 7} — each cell has only two of the three digits, but between them the digits 2, 5, and 7 are exhausted.
A less obvious shape: three cells with all three digits as their full possible set. {2, 5, 7}, {2, 5, 7}, {2, 5, 7}. The reasoning still holds — the three cells together must hold the three digits — but the pattern is harder to spot because the cells look identical, and there's no immediate visual cue that they form a triple.
Why "kakuro triple" rather than "naked triple"
Like the kakuro pair versus naked pair distinction, the kakuro triple operates on runs rather than Sudoku units, and the run's cell count and target interact with the triple's claim. After firing the triple, the run's effective target has dropped by the sum of the three digits, and the remaining cells now solve a reduced sub-problem with fewer cells and a smaller target.
That smaller sub-problem often becomes a unique sum that wouldn't have fired on the original run. A 5-cell run with target 25 might not have a unique combination, but after a triple claims 14 of the target across 3 cells, the remaining 2 cells have a target of 11 — still not unique on its own, but combined with the triple's eliminated digits and any cross-references on the remaining cells, the puzzle often resolves.
When you'll see it
Kakuro triples are less common than kakuro pairs because three cells with the right cross-reference pattern is more restrictive than two. They tend to appear on harder kakuros after several rounds of cross-reference and pair eliminations have narrowed cell sets to small triples. The signature is three cells in the same run whose possible sets all draw from the same three digits — sometimes obvious, sometimes only visible after a careful read of the run's pencil marks.
The pattern generalises to quads (four cells, four digits) but those are rare enough that most published kakuros don't require them.
See also
- 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.
- Naked triple— Three cells in the same unit whose candidates collectively use only three digits. Together they claim those digits across the 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.
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.