Sudoku rules

The whole game in one sentence

Fill the 9×9 grid so that every row, every column and every 3×3 box contains each digit from 1 to 9 exactly once. That is the entire rulebook. Everything else people say about sudoku is technique, not rules.

The digits printed on the board at the start never move. You only add the missing ones, in any order you like.

The three constraints, one at a time

• Row — nine cells across. Nine different digits, no repeats.
• Column — nine cells down. Same requirement.
• Box — one of the nine 3×3 squares marked by thicker lines. Same requirement again.

Every cell belongs to all three at once, and that overlap is where the whole game lives. A cell that sees a 4 in its row, a 7 in its column and a 2 in its box cannot hold any of those three digits.

What is not a rule

Beginners often assume constraints that do not exist:

• Diagonals do not matter. A diagonal may repeat digits freely. (Sudoku X, a variant, adds that rule — plain sudoku does not.)
• There is no arithmetic. Nothing has to add up to anything. The digits are just nine distinct symbols; you could play with nine colours instead.
• Order does not matter. You may fill cells in any sequence. There is no penalty for jumping around the grid.
• Guessing is never required. Every board here has exactly one solution and is reachable by logic alone. If you feel you have to guess, a wrong digit went in earlier.

That last point is the one that separates a fair puzzle from a bad one. A board with two possible solutions is broken, no matter how nicely it is presented.

What counts as a mistake here

On Brain Arena a mistake means a digit different from the one in the solution — not merely a digit that clashes with what is already on the board. The difference matters: a wrong digit that does not clash yet would otherwise be silently accepted and only punish you ten moves later, in a different place.

You have three mistakes per board. A wrong digit costs one life and stays marked in red with a strikethrough until you fix it. Undo removes the mark but does not give the life back — otherwise the limit would be decorative.

How to actually start

1. Pick the digit that appears most often on the board and find its remaining places. More copies already placed means fewer options left.
2. Scan box by box, not cell by cell. Check which rows and columns already contain that digit; often exactly one free square survives.
3. Look for a cell with one option. A cell that sees eight different digits has only one possible answer.
4. Close any unit missing a single digit — the cheapest points on the grid, and each one tends to create another.

That is enough to finish every easy board. When it stops being enough, the named techniques begin — they are collected on the strategy page.