Kakuro
How to Play Kakuro
Kakuro (交叉和) is a cross-sum number puzzle — think of it as a numeric crossword. The grid is made of wall cells and empty white cells. Each wall cell can carry a clue: a number in its top-right corner is the sum of the horizontal run of white cells to its right, and a number in its bottom-left corner is the sum of the vertical run of white cells below it. Fill every white cell with a digit from 1 to 9 so that each run adds up to its clue, and — this is the key rule — no digit repeats within a single run. Click a white cell to select it, then tap a number on the pad or press 1–9; use erase (or Backspace) to clear a mistake. Every puzzle here has exactly one unique solution, so disciplined logic always beats guessing.
Solving Techniques
- Unique sum combinations: Some runs have only one possible set of digits. A 2-cell run summing to 3 must be {1,2}; a 3-cell run summing to 6 must be {1,2,3}; a 2-cell run summing to 17 must be {8,9}. Learning these forced combinations cracks the corners open.
- Cross-referencing: A white cell sits on both an across run and a down run. Intersect the candidate sets of the two runs — the cell can only hold a digit that is possible for both, which often leaves just one option.
- The 45 rule: Every full row or column region of white cells has known totals. When a run is nearly complete, the missing cell equals the clue minus the digits already placed — a direct, no-guess deduction.
- Pencil the candidates: For each cell, note which digits its across and down clues still allow. As you place digits, distinct-digit and sum constraints eliminate candidates, and forced cells reveal themselves in a chain.
- High and low extremes: Long runs with very high or very low sums are tightly constrained — a 3-cell run summing to 24 must be {7,8,9}. Anchor the grid on these near-forced runs first, then let their digits propagate.
How do you solve Kakuro faster? Start with the runs that have unique combinations (the smallest and largest sums), pencil in candidates, then cross-reference intersections until forced cells cascade. Because every valid Kakuro has a single solution, every digit you place should be one you can justify — no guessing required. The leaderboard ranks solves by completion time, so the fastest, cleanest logical path wins.