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How to play Kakuro (Cross Sums)

Kakuro, also called Cross Sums, is a number crossword. Each clue cell shows a target: the number in the upper-right is the sum of the run to its right, and the number in the lower-left is the sum of the run below it. Fill the white cells with 1–9 so every run hits its sum without repeating a digit.

1. 1Read the clues. A clue in the upper-right of a dark cell is the sum of the white run to its right; a clue in the lower-left is the sum of the run going down.
2. 2Fill runs with 1–9. Each white cell holds a digit 1–9. The digits in a single run must add up to that run's clue.
3. 3Never repeat within a run. A digit can appear only once per run, though the same digit can appear in crossing runs.
4. 4Use magic combinations. Some sums force the digits: a 2-cell run summing to 3 is {1,2}; a 3-cell run summing to 6 is {1,2,3}. Start there.
5. 5Cross-check intersections. Each white cell sits in an across run and a down run — use both clues to pin the digit.

Tips & strategy

Begin with the most constrained runs — short runs with extreme sums (very low or very high) have only one possible digit set. Where a forced across-run crosses a forced down-run, the shared cell is often immediately solvable, and that cascades through the grid.