2026-09-22
Kakuro looks like a crossword but plays like arithmetic. Every run of white cells must sum to its clue using digits 1–9, with no digit repeated inside a run. Most grids fall to a handful of repeatable techniques.
Some clues have only one possible set of digits. A 2-cell run of 3 must be {1,2}; a 2-cell 17 must be {8,9}; a 3-cell 6 must be {1,2,3}. These "magic" combos give you digits — or at least a tight candidate set — for free. The extremes are the most valuable: 3, 4, 16, 17 in two cells; 6, 7, 23, 24 in three.
Every cell belongs to two runs: one across, one down. If the across run needs {1,2} and the down run needs {8,9}, the intersection is impossible — a fast contradiction check. More usefully, if across allows {1,2,4} and down allows {2,4,9}, the cell can only be 2 or 4. Do this for every cell where two constrained runs meet.
If a 3-cell run totals 10, the digits sum to 10 — but if you can prove one cell is even (say, from a crossing run), the candidates collapse. Work per-cell: list what each cell can be from the across run, then filter by the down run, then filter again by what digits the run still needs.
After each pass, look for cells with exactly one legal digit. Fill it, remove that digit from both runs, and repeat. Kakuro cascades: one solved cell frequently unlocks four or five more. Stuck grids usually mean you stopped doing passes, not that the puzzle is hard.
In a run with some cells filled, subtract the placed digits from the clue — the remaining cells must sum to the remainder. A 4-cell 20 with a 9 and 7 placed leaves 4 for two cells, so {1,3} — and 3 can't repeat if it's already in the run, so the order matters.
Ready to try? Play Kakuro — or test the same digit logic on Calcudoku, which swaps sums for cage arithmetic.