What Is Sudoku?

Sudoku is a logic-based number-placement puzzle played on a 9×9 grid subdivided into nine 3×3 regions, called boxes. The objective is to fill every empty cell with a number from 1 to 9 so that each row, each column, and each 3×3 box contains every digit exactly once. No arithmetic is required — only pure logical deduction. The digits 1–9 are symbols, not values: a Sudoku puzzle could use letters A–I or any nine distinct glyphs without changing the puzzle.

How Sudoku works

Every valid Sudoku puzzle starts with a set of given digits (also called clues), typically between 17 and 45 cells, with the remaining cells empty. A well-formed Sudoku has exactly one solution reachable through pure logical deduction — no guessing is required, and there is exactly one valid way to fill the grid. The 17-clue minimum was proven by Gary McGuire's exhaustive computer search in 2012; no Sudoku puzzle with fewer than 17 clues has a unique solution.

Origin and naming

The modern Sudoku puzzle was designed in 1979 by Howard Garns, an American architect, who published it under the name Number Place in Dell Pencil Puzzles & Word Games. The puzzle became popular in Japan after Nikoli, a puzzle publisher in Tokyo, renamed it Sūji wa dokushin ni kagiru — 'the digits must be single' — abbreviated to Sudoku in 1986. Sudoku became a global phenomenon in late 2004 when Wayne Gould convinced The Times of London to publish the puzzle daily, and within months it appeared in newspapers worldwide.

The three core rules

Sudoku has just three rules, but they interact to produce remarkable depth:

1. Row constraint: each row must contain the digits 1–9, each appearing exactly once.
2. Column constraint: each column must contain the digits 1–9, each appearing exactly once.
3. Box constraint: each 3×3 sub-grid (box) must contain the digits 1–9, each appearing exactly once.

Together these constraints mean that a digit placed in any cell must be unique within three regions simultaneously — its row, its column, and its box. The intersection of these three constraints is what creates Sudoku's logical depth and why the same digit cannot repeat within sight of itself.

Why Sudoku is mathematical (and why it is not)

Sudoku is often described as a 'maths puzzle' because it uses digits, but it requires no arithmetic. The puzzle could be re-symbolised with the letters A–I, with shapes, or with colours and the logic would remain identical. What makes Sudoku mathematical is its combinatorial structure: the puzzle is an instance of an exact cover problem, related to graph colouring and Latin square theory, with the box constraint added.

Sudoku in cognitive research

Regular Sudoku solving is associated with improved working memory and processing speed in adults aged 50+, according to studies on puzzle-based cognitive training. Sudoku develops the same pattern-recognition skill as scientific debugging and structured problem-solving — both involve iteratively narrowing a solution space through constraint satisfaction.

Sudoku variants

Beyond Classic 9×9 Sudoku, dozens of variants add or modify constraints: Killer Sudoku adds cage sums, Diagonal Sudoku adds two diagonal constraints, Hyper Sudoku adds four additional 3×3 boxes, X-Sudoku constrains both diagonals to contain 1–9, and Samurai Sudoku overlaps five 9×9 grids. Mini Sudoku (4×4) and Kids Sudoku (9×9 with friendly clue placement) are entry-level variants designed for newcomers.

Browse all Sudoku puzzle formats