Sudoku Rules Explained

Sudoku has just three rules. They are easy to state, but understanding exactly what they mean — and why they work together — will make you a significantly better solver. This article explains every rule in full, with no assumptions about prior knowledge.

The Grid

A standard sudoku puzzle is played on a 9×9 grid containing 81 cells. The grid is subdivided into nine 3×3 boxes (sometimes called regions, blocks, or squares). These boxes are arranged in a 3×3 pattern, giving the grid its characteristic appearance.

Every cell in the grid belongs to exactly three groups simultaneously:

• One of the nine rows (horizontal lines)
• One of the nine columns (vertical lines)
• One of the nine 3×3 boxes

This triple membership is the heart of sudoku. Every constraint you apply to a cell draws from all three groups at once.

The Three Rules

Rule 1: Every Row Must Contain 1–9

Each of the nine horizontal rows must contain all nine digits — 1, 2, 3, 4, 5, 6, 7, 8, and 9 — with no digit appearing more than once. Since each row has exactly nine cells and must contain exactly nine distinct digits, every row is a complete set of 1–9 in some order.

Rule 2: Every Column Must Contain 1–9

Each of the nine vertical columns must also contain all nine digits, with no repeats. The same logic applies: nine cells, nine distinct digits, one of each.

Rule 3: Every 3×3 Box Must Contain 1–9

Each of the nine 3×3 boxes must contain all nine digits, with no repeats. The nine cells inside each box hold exactly one of each digit from 1 to 9.

What the Rules Mean Together

The power of sudoku comes from how these three rules interact. Because every cell belongs to a row, a column, and a box simultaneously, placing a single digit has ripple effects across the entire grid.

For example: if you place a 7 in the top-left cell of the grid, that 7 eliminates 7 as a possibility for every other cell in row 1, every other cell in column 1, and every other cell in the top-left 3×3 box. One placement, 20 eliminations.

This cascading effect is what makes sudoku solvable through pure logic. As you fill in more cells, the remaining empty cells become more and more constrained, until each one has only one valid digit left.

The Clues

At the start of a puzzle, some cells are already filled in. These pre-filled numbers are called clues (or givens). Clues are fixed — you cannot change them.

The number of clues affects the difficulty of the puzzle. Easy puzzles typically have 35 or more clues, leaving fewer empty cells to deduce. Evil or expert puzzles may have as few as 20–22 clues, requiring long chains of logic to progress.

Mathematically, a valid sudoku puzzle must have at least 17 clues to guarantee a unique solution. Puzzles with fewer than 17 clues either have no solution or have multiple solutions — neither of which counts as a proper sudoku.

The One-Solution Rule

A properly constructed sudoku puzzle has exactly one solution. This is not just a convention — it is a requirement. If a puzzle has two or more valid solutions, it is considered flawed.

This rule has an important practical implication: you should never need to guess. If the puzzle is valid, every empty cell can be determined through logic alone. When experienced solvers appear to "guess," they are actually applying advanced techniques that eliminate all but one possibility — the reasoning is just happening faster than it looks.

What Sudoku Is Not

A few common misconceptions worth clearing up:

• Sudoku is not a math puzzle. The digits 1–9 are used purely as symbols. You could replace them with letters A–I or any nine distinct symbols and the puzzle would work identically. No arithmetic is involved.
• Sudoku does not require memorization. Every step follows logically from the current state of the grid. You don't need to remember previous states or track complex sequences.
• Sudoku is not about speed — at first. Beginners who rush make errors. Accuracy comes before speed. Speed is a byproduct of recognizing patterns quickly, which comes with practice.

Variants

The rules above describe classic sudoku, the standard form played worldwide. Many variants exist — Killer Sudoku adds cage constraints, Diagonal Sudoku adds two diagonal constraints, and Mini Sudoku uses a 6×6 grid — but all variants build on the same three foundational rules. Master the classic form first.

Start Playing

Now that you know the rules, the fastest way to internalize them is to play. Easy puzzles are ideal for beginners — the clues are generous and the logic steps are short and clear.

Play a free Easy Sudoku puzzle →

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