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The Complete Rules of Sudoku
The complete rules of Sudoku explained simply. Learn the three basic rules, how the grid works, the unique-solution guarantee, and common rule variants.
Sudoku has just three rules. They are simple to state but produce remarkable logical depth when combined. This page explains the rules, what makes a valid Sudoku, common rule variants, and the small set of edge cases that trip up beginners.
The grid
A Classic Sudoku grid is 9 cells wide by 9 cells tall — 81 cells in total. The grid is divided into nine 3×3 sub-grids called boxes (or regions). Each row, each column, and each box has nine cells.
The three rules
- Row rule: each of the nine rows must contain the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 — each appearing exactly once.
- Column rule: each of the nine columns must contain the digits 1–9 — each appearing exactly once.
- Box rule: each of the nine 3×3 boxes must contain the digits 1–9 — each appearing exactly once.
A digit placed in any cell must be unique across three regions: its row, its column, and its 3×3 box. These three constraints interact to determine where each digit must go.
Given digits
A Sudoku puzzle begins with some cells pre-filled. These are called given digits, givens, or clues. The solver's task is to fill every other cell so that the three rules are satisfied. The given digits are fixed — they cannot be changed.
The unique-solution guarantee
A well-formed Sudoku puzzle has exactly one valid solution that can be reached through pure logical deduction without guessing. Puzzles with multiple solutions or no solutions are considered invalid — a single unique solution is a defining property of Sudoku.
The minimum number of given digits for a unique solution is 17, proven by Gary McGuire's 2012 exhaustive computer search. Puzzles with 16 or fewer givens always have multiple solutions and are therefore not valid Sudoku.
What is not in the rules
Sudoku does not require arithmetic. Digits do not need to sum to anything. The puzzle is purely about position and presence. Replacing 1–9 with letters A–I would produce an identical puzzle.
Sudoku does not have a 'snake' rule, a 'no consecutive' rule, or a 'diagonal' rule in the standard format. Adding any of those creates a variant, not Classic Sudoku.
Common variants and their extra rules
Mini Sudoku (4×4): Same rules but with digits 1–4 only, four 2×2 boxes, and four rows/columns.
Diagonal (X) Sudoku: Both main diagonals must also contain 1–9 each exactly once.
Killer Sudoku: Cells are grouped into 'cages' with a sum constraint; digits within a cage cannot repeat and must sum to the cage total.
Hyper (Windoku) Sudoku: Four additional 3×3 boxes added in the centre regions, each constrained to contain 1–9.
Sudoku 16×16 (Hexadoku): 16×16 grid with hexadecimal digits 0–F, sixteen 4×4 boxes.
Common edge cases
Can the same digit appear twice in a row? No. Each digit appears exactly once in each row.
Can a 3×3 box contain duplicates? No. Each digit appears exactly once in each box.
Can the diagonals contain duplicates in Classic Sudoku? Yes. Classic Sudoku has no diagonal constraint. Only Diagonal/X-Sudoku adds it.
Are zeros allowed? No. Sudoku uses only digits 1–9 (or 1–4 in Mini Sudoku).
FAQ
Sudoku Rules — Frequently Asked Questions
What are the rules of Sudoku?
There are three: each row must contain the digits 1–9 exactly once, each column must contain the digits 1–9 exactly once, and each 3×3 box must contain the digits 1–9 exactly once.
Can a number repeat in a Sudoku row?
No. A digit may appear only once per row, once per column, and once per 3×3 box. Any repeat makes the grid invalid.
Can you use zero in Sudoku?
No. Standard Sudoku uses the digits 1 to 9 only. Zero is never placed in a 9×9 grid, and 4×4 mini Sudoku uses 1 to 4.
Are diagonals part of the Sudoku rules?
Not in standard Sudoku. Diagonal constraints belong to a variant called Sudoku X, which is a separate puzzle type.
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