Sudoku Rules: Everything You Need to Know

Sudoku has some of the simplest rules in all of puzzle-dom - yet those three rules create endless complexity. This page explains the complete rules of standard 9×9 Sudoku, clears up common misconceptions, and covers the most popular rule variations.

The Three Fundamental Rules

Standard Sudoku has exactly three rules. Every puzzle follows these rules, regardless of difficulty level:

1. Each row contains the digits 1-9 exactly once

A Sudoku grid has 9 horizontal rows. In a completed puzzle, every row contains each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 - no digit is repeated, and no digit is missing.

2. Each column contains the digits 1-9 exactly once

The same constraint applies to the 9 vertical columns. Read any column from top to bottom, and you will find each digit from 1 to 9 appearing exactly once.

3. Each 3×3 box contains the digits 1-9 exactly once

The grid is divided into 9 non-overlapping 3×3 boxes (also called blocks or regions), marked by thicker borders. Each box must also contain every digit from 1 to 9 without repeats.

That is it - three rules. The interplay between rows, columns, and boxes is what creates the logical complexity that makes Sudoku so compelling.

Grid Structure Explained

Understanding the grid layout is essential to applying the rules correctly.

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Cells - The grid contains 81 individual cells (9 rows × 9 columns). Each cell holds exactly one digit in the completed puzzle.

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Rows - 9 horizontal lines of 9 cells each, typically labeled row 1 (top) through row 9 (bottom).

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Columns - 9 vertical lines of 9 cells each, typically labeled column 1 (left) through column 9 (right).

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Boxes - 9 groups of 3×3 cells. They do not overlap, and every cell belongs to exactly one box. The boxes are usually numbered 1-9, reading left-to-right, top-to-bottom.

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Givens (Clues) - The pre-filled digits that define the puzzle. A valid puzzle has exactly one solution. The number of givens determines difficulty: easy puzzles have 36-45, while evil puzzles can have as few as 17.

How Digits Work in Sudoku

Each digit from 1 to 9 appears exactly 9 times in a completed Sudoku grid - once per row, once per column, and once per box. This means there is no "special" digit; all nine are equally distributed.

An important consequence: if you know 8 of the 9 digits in any row, column, or box, the 9th is automatically determined. This is the basis of the "last remaining cell" solving technique.

The digits are arbitrary symbols. You could use the letters A through I, the colors of the rainbow plus two more, or any nine distinct symbols. The puzzle logic would be identical.

Common Misconceptions

"You need math skills to play Sudoku"

False. Sudoku involves zero arithmetic. You never add, subtract, multiply, or divide. The digits are just symbols - the puzzle is purely about logic and pattern recognition.

"There can be multiple solutions"

A properly constructed Sudoku puzzle has exactly one unique solution. If a puzzle has multiple solutions, it is considered invalid. All puzzles on Sudoku91 are computer-validated to ensure a single solution.

"You sometimes have to guess"

Never. Every valid Sudoku puzzle can be solved through logic alone. If you feel like guessing, it means there is a technique you have not applied yet - not that the puzzle requires luck.

"The more givens, the easier the puzzle"

Usually true, but not always. The placement of givens matters as much as the quantity. A puzzle with 30 well-placed givens can be easier than one with 28 poorly placed ones. That said, as a general rule, more givens means fewer logical steps to solve.

"Sudoku was invented in Japan"

Partially true. The modern Sudoku format was first published as "Number Place" by Howard Garns in Dell Magazines (USA) in 1979. It was later introduced to Japan by Nikoli in 1984, where it gained the name "Sudoku" and became a global phenomenon.

Popular Sudoku Variations

While standard 9×9 Sudoku is the most popular format, many variations exist. Here are some of the most well-known:

Mini Sudoku (4×4 or 6×6)

Smaller grids using digits 1-4 or 1-6. Great for children or quick puzzles. A 6×6 grid uses 2×3 boxes.

Killer Sudoku

Combines Sudoku with arithmetic. Dashed "cages" group cells whose digits must sum to a given total. The standard Sudoku rules still apply, but no digit repeats within a cage.

Diagonal Sudoku (Sudoku X)

Adds a fourth constraint: the two main diagonals must also contain the digits 1-9 exactly once. This extra rule significantly changes the solving logic.

Samurai Sudoku

Five overlapping 9×9 grids arranged in an X pattern. The overlapping regions must satisfy the rules for both of the grids they belong to. Much larger and more complex than standard Sudoku.

Ready to Play?

Now that you understand the rules, there is only one thing left to do - put them into practice.

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FAQ

What are the basic rules of Sudoku?

Sudoku has three rules: each row, each column, and each 3×3 box must contain the digits 1-9 exactly once with no repeats. That is the entire ruleset.

What is the 3 rule in Sudoku?

The "3 rule" refers to the third constraint in Sudoku: each 3×3 box (the nine regions marked by thicker borders) must contain every digit from 1 to 9 without repetition.

How many digits are in a Sudoku puzzle?

A completed Sudoku grid contains 81 digits (9 rows × 9 columns). Each of the digits 1-9 appears exactly 9 times. A starting puzzle has some cells pre-filled (givens) with fewer cells for harder puzzles.

Can a Sudoku have more than one solution?

A valid Sudoku puzzle must have exactly one unique solution. Puzzles with multiple solutions are considered poorly constructed. All puzzles on Sudoku91 are validated to ensure a single solution.