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.
A run is the kakuro equivalent of a Sudoku unit. It's a sequence of white cells extending horizontally or vertically from a clue cell, ending at the next dark cell or the edge of the grid. The clue cell carries a target sum; the run's white cells must add to that sum, and no digit can repeat within the run.
How runs structure the puzzle
Every white cell in a kakuro grid belongs to exactly two runs — one horizontal, one vertical — and the cell's digit must satisfy both runs' constraints simultaneously. The horizontal run requires the cell's digit to combine with the other horizontal cells to sum to one target without repeats; the vertical run requires the same with a different target and a different set of partners.
This dual-membership is what makes kakuro reasoning work. A cell whose horizontal run has narrowed to two possible digits and whose vertical run has narrowed to a different two digits can only take a digit appearing in both narrowed sets — typically just one. That intersection move is called cross-reference and runs through nearly every kakuro deduction.
Run length and the digit pool
Kakuro runs can be any length from 2 to 9 cells. A 2-cell run with a small target (say 3) has limited combinations — only {1, 2}. A 9-cell run is exhausting: it must contain every digit from 1 to 9 exactly once, and its sum is necessarily 45.
Most kakuro deduction lives in the middle range. A 3-cell run with target 7 has only one combination — {1, 2, 4} — making it a unique sum. A 4-cell run with target 14 has many combinations and contributes less directly to the deduction. The kakuro-sum-combinations reference table catalogues which (length, target) pairs have unique or near-unique combinations.
Why "run" rather than "row" or "column"
Kakuro grids don't have rigid row-and-column structure the way Sudoku does. A kakuro row might contain several runs separated by dark cells, each independently constrained. The same row can hold a horizontal run of length 3 followed by another of length 5, with different targets. Run is the unit of sum-and-no-repeats reasoning, distinct from the geometric row or column.
In practice, when a kakuro player says "the run going down from this clue" or "this column's first run," they're naming the specific cell sequence under one clue, not the whole row or column. The vocabulary maps cleanly onto how the puzzle is solved.
See also
- Kakuro— A Japanese number-placement puzzle. Cross-sums act like a crossword grid; players fill white cells with digits 1–9 so each run sums to its target without repeating a digit.
- Clue cell— The dark cell in a kakuro grid carrying the target sums for the runs extending from it — usually one or two numbers separated by a slash.
- Entry cell— A white cell in a kakuro grid that the player fills with a digit. Each entry cell belongs to exactly two runs — one horizontal, one vertical — and must satisfy both.
- Kakuro sum combinations— The reference table mapping each (cell-count, target-sum) pair to its valid digit combinations. The foundational lookup that anchors most kakuro deduction.
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.