Sudoku rules, in full

The grid

A standard Sudoku is a 9×9 grid, subdivided into nine 3×3 regions called boxes. That gives 81 cells total. Some cells are pre-filled with digits 1–9 — these fixed cells are called the givens and cannot be changed. Every remaining cell is empty at the start of the puzzle, and your job is to place a digit in each of them.

The three constraints

You fill every empty cell so that all three of the following are true simultaneously:

• Each row contains the digits 1–9 exactly once (no repeats).
• Each column contains the digits 1–9 exactly once (no repeats).
• Each 3×3 box contains the digits 1–9 exactly once (no repeats).

That's the entire rule set. There is no arithmetic. The digits could equally well be letters (A–I) or colors — the shape of the constraint is what makes the puzzle work. Every cell is part of exactly three units: one row, one column, and one box, and each of those units must satisfy the "1–9 exactly once" rule.

Uniqueness — why you never have to guess

A well-formed Sudoku has exactly one solution. That is not a suggestion; it's the defining property of the puzzle. If a board admits two or more solutions, it isn't a Sudoku — it's a broken puzzle. Zeloku verifies uniqueness computationally when each puzzle is generated: any board that our solver finds a second solution for is discarded before it ever reaches the site.

The practical consequence: avoid random guesses. Start with deductions from the givens, add pencil-marks when the board stalls, and work through named techniques systematically. Some positions require methods beyond Zeloku's current hint engine; the techniques library introduces the main patterns.

The minimum-clue rule

How few givens can a Sudoku have and still be unique? In 2012, mathematicians at University College Dublin proved the answer: 17. There is no 9×9 Sudoku with 16 or fewer givens that has a unique solution — such a board is always ambiguous. In practice, well-designed puzzles hover in these ranges:

Sudoku variants

The 9×9 board is the classic. The rule shape — "each digit exactly once in each unit" — generalises cleanly to smaller and larger boards, and to boards with extra constraints. The variants you'll actually see online:

• 4×4 Sudoku — digits 1–4 in 2×2 boxes. Great for kids ages 5–7. See Kids Sudoku.
• 6×6 Sudoku — digits 1–6 in 2×3 boxes. A bridge to 9×9 for kids 7–10 or a fast warm-up.
• Killer Sudoku — 9×9 with extra "cages" that must sum to a given target using distinct digits. Full rules on the Killer Sudoku rules page.
• Diagonal (X) Sudoku — the two main diagonals become additional units. Both must also contain 1–9 exactly once.
• Mini Sudoku — an umbrella term for 4×4 and 6×6 boards.
• Irregular / Jigsaw Sudoku — 9×9 with the nine boxes replaced by nine irregularly-shaped regions of nine cells each. Rows and columns unchanged.
• Samurai Sudoku — five overlapping 9×9 boards sharing corner boxes. Play them one at a time; the shared boxes propagate.

What is not a Sudoku rule

Several common beliefs about Sudoku are folklore, not rules:

• "Diagonals must contain 1–9 exactly once." — Only true in Diagonal (X) Sudoku. In classic Sudoku, diagonals are unconstrained.
• "Sudoku uses arithmetic." — Only in variants like Killer or Kakuro. Classic Sudoku is pure logic; no adding.
• "Guessing is the best way forward." — Random guesses are difficult to audit. Candidate elimination, named techniques or systematic search produce a traceable path instead.
• "There must be an even number of clues." — There is no such requirement. Clue count depends on difficulty, not parity.

Reading Sudoku notation

You'll sometimes see boards written as a single 81-character string, with 0 or . for empty cells. Reading row by row, left to right, top to bottom. For example:

530070000
600195000
098000060
800060003
400803001
700020006
060000280
000419005
000080079

...is a valid Easy 9×9 puzzle. Zeloku's solver accepts this notation directly — paste any 81 characters and step through the solve.

From the rules to your first solve

Knowing the rules is one minute of reading. Actually solving your first board takes about five. The how to play Sudoku guide walks you through the two techniques (naked single, hidden single) that solve every Easy board. When those feel automatic, browse the learn hub for the six intermediate and advanced techniques that carry you through Hard and Expert.

Sudoku rules — frequently asked questions