Donka Puzzle Co.

How to Play Sudoku

Sudoku has one rule, and everything else is a consequence of it. This guide covers the rule, the grid vocabulary you'll see in every other guide on this site, and the first two solving moves worth learning.

The one rule

A Sudoku grid is nine rows by nine columns, subdivided into nine 3×3 boxes. Some cells arrive already filled in — those are the givens, and they never change. Your job is to fill every empty cell so that:

That's the whole game. There is no arithmetic — the digits are just nine distinct symbols, and you could play with nine colours or nine letters and nothing would change. Rows, columns and boxes are collectively called units, and there are 27 of them on a board. Every cell belongs to exactly three: one row, one column, one box.

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The three constraints, shaded together: the top row, the fifth column, and the bottom-right box. Each must end up holding 1 through 9 exactly once.

Every real puzzle has exactly one answer

A properly constructed Sudoku has precisely one solution, and — this is the part that matters — that solution can be reached by pure deduction. You never need to guess. If you find yourself picking a digit to see whether it works out, either there's a deduction you haven't spotted yet or you've already made a mistake somewhere above.

The puzzles on this site are all generated with a solver that verifies uniqueness before a board is served, so if you're stuck, the logic is there. It's just hiding.

Reading a cell's candidates

The single most useful habit in Sudoku is thinking in candidates: for any empty cell, the set of digits that could still legally go there. To work them out, list 1 through 9 and cross off everything already present in that cell's row, its column, and its box.

Say a cell sits in a row that already contains 1, 4 and 8; a column containing 4, 6 and 9; and a box containing 8 and 2. Strike out 1, 2, 4, 6, 8 and 9, and you're left with 3, 5 and 7. Those three are the cell's candidates. Writing them into the cell as small pencil marks — the Notes button on this site, or the N key — is how you keep track without recomputing every time.

Worth knowing

Beginners often avoid pencil marks because they feel like cheating or like clutter. They are neither. Every solving technique past the very simplest is expressed in terms of candidates, so refusing to write them down caps how far you can get.

Your first move: scan for forced placements

Pick a digit — 5, say — and look at where the 5s already sit. Each existing 5 rules out its entire row, its entire column, and its entire box. Sweep those exclusions across the grid and you will often find a box where only one cell survives. That cell must be a 5.

This is called crosshatching, and on an easy puzzle it will carry you most of the way to a finished grid on its own. It's covered properly in the scanning guide.

Your second move: look for cells with one candidate

The mirror image of scanning. Instead of asking "where can this digit go?", ask "what can go in this cell?" If a cell's row, column and box between them account for eight different digits, only one candidate remains and it's forced. That's a naked single.

These two moves — scanning by digit, and checking cells for a lone candidate — solve every Easy puzzle and most Medium ones. See naked and hidden singles for the full treatment, including the sneakier variant where a digit is forced in a cell that still has several candidates written in it.

Practical habits

Playing on this site

Click or tap a cell to select it, then press a number key or use the on-screen pad. Toggle Notes to enter pencil marks instead of a final digit. Erase clears a cell; Hint reveals one correct digit if you're properly stuck. The Daily Challenge is the same board for every visitor and resets at midnight, so a streak is a genuine record of consecutive days solved. Practice mode is unlimited across four difficulties.

Read next Scanning and crosshatching →