Kakuro
Play Kakuro (cross sums) puzzles in your browser. Fill each run with digits 1–9, no repeats, matching every clue. Easy, medium and hard grids, instantly regenerated.
Click a cell, then type 1–9 (or use the pad). Arrow keys move, Backspace clears. Each row must sum to its right clue; each column to its down clue. No digit repeats inside a row or column.
The rules
Kakuro — literally kasan kurosu, “addition cross” — is a crossword done with digits. Every white cell holds a digit 1–9. Each horizontal “run” of white cells must sum to the clue shown in the upper-right triangle of the black cell on its left. Each vertical run must sum to the clue in the lower-left triangle of the black cell above it.
The catch: no digit can repeat inside a single run. So a 2-cell run summing to 4 must be {1, 3}, a 2-cell run summing to 17 must be {8, 9}, and so on. These “unique-sum” combinations are the heart of every deduction.
Magic combinations cheat sheet
A few clue/length pairs allow only one set of digits. Memorise these and you'll pencil in entire runs at a glance.
| Length | Sum | Only digits |
|---|---|---|
| 2 | 3 / 4 / 16 / 17 | {1,2} / {1,3} / {7,9} / {8,9} |
| 3 | 6 / 7 / 23 / 24 | {1,2,3} / {1,2,4} / {6,8,9} / {7,8,9} |
| 4 | 10 / 11 / 29 / 30 | {1,2,3,4} / {1,2,3,5} / {5,7,8,9} / {6,7,8,9} |
| 5 | 15 / 16 / 34 / 35 | {1..5} / {1,2,3,4,6} / {4,6,7,8,9} / {5,6,7,8,9} |
| 6 | 21 / 39 | {1..6} / {4..9} |
How to solve
- Find magic runs first. Any clue that's an extreme (very low or very high sum) for its length pins the digit set even if not their order.
- Cross-reference. A cell sits at the intersection of one horizontal and one vertical run. Intersect the two candidate sets — often only one digit survives.
- Track forbidden digits. In a run, once you place a digit, you ban it from the rest of that run and adjust remaining sums accordingly.
- Look for sum splits. For a 3-cell run of 7 = {1,2,4}, if one cell can't be 4 (because its column says so), it must be 1 or 2, which often forces the rest.
History & trivia
Kakuro was invented in 1966 by Canadian Jacob Funk as Cross Sums for Dell Magazines, then renamed and popularised in Japan by publisher Maki Kaji's Nikoli in 1980 — the same company that gave Sudoku its name. In Japan it ranks second only to Sudoku in popularity; the all-time hardest puzzles use grids 16×16 and larger and rely on intersecting magic combinations through dozens of runs.