Kakuro

Kakuro is a logic puzzle played on a grid of white and black cells. The goal is to fill each white cell with a digit from 1 to 9 so that the digits in each horizontal or vertical run sum to the clue indicated by the adjacent black cell. Digits may not repeat within a single run.

Each black cell may contain two clues: an across clue to the right and a down clue beneath. If a run has only a down clue, it will not have an across clue, and vice versa. White cells belong to both an across run and a down run, so the digits chosen must satisfy both sums.

Solving Kakuro relies on arithmetic and logical deduction rather than guessing. For each run, possible combinations of distinct digits that sum to the clue are enumerated. The candidate digits intersect between the perpendicular runs, gradually narrowing possibilities until cells are determined. Pencil marks or notes are often used to track options.

Kakuro originated in Japan and gained international popularity through puzzle books and magazines in the late 20th century. In English-language publications, it is sometimes called Cross Sums. The puzzle shares a family resemblance with Sudoku in its reliance on deduction and its grid-based structure, but it emphasizes sums and digit uniqueness within runs.