Sudoku

Sudoku is a logic-based number-placement puzzle. The standard version uses a 9x9 grid divided into nine 3x3 subgrids. The objective is to fill the grid with digits 1 through 9 so that each row, column, and 3x3 subgrid contains each digit exactly once. The puzzle is typically solved by deduction rather than calculation, and many variants exist with different grid sizes or subgrid shapes.

The modern Sudoku has roots in earlier number-placement concepts and Latin squares. It was popularized in Japan by the puzzle publisher Nikoli in the 1980s, and gained worldwide attention in the 2000s. The form known in the United States as Number Place appeared in 1979, and the name Sudoku—short for the Japanese phrase Sūji wa dokushin ni kagiru, meaning “the digits must be single”—became widely used as the puzzle spread globally.

Solving Sudoku relies on logical reasoning. Common techniques include scanning rows, columns, and subgrids to identify possible candidates, cross-hatching, and recognizing forced placements. More challenging puzzles may require advanced methods such as X-Wing, Swordfish, hidden pairs, or computer-based backtracking solvers. Most published puzzles are designed to have a unique solution.

Beyond recreational play, Sudoku is used in education and computer science as an example of a constraint satisfaction problem. Solving approaches range from manual deduction to algorithmic strategies like backtracking and more sophisticated techniques such as dancing links. The puzzle has inspired variants, competitions, and a substantial body of research and practice in logic and problem solving.