How to play Sudoku

The rule

A Sudoku is a 9×9 grid divided into nine 3×3 boxes. Some cells start with digits in them. Fill in the rest so that:

• every row contains the digits 1 to 9, each exactly once
• every column contains the digits 1 to 9, each exactly once
• every 3×3 box contains the digits 1 to 9, each exactly once

That is the whole game. There is no arithmetic — the digits are just nine distinct symbols, and you could play with nine colours and change nothing. Anyone who tells you Sudoku is a maths puzzle has not looked closely.

A properly made puzzle has exactly one solution, reachable by logic alone. That matters more than it sounds: it means you should never have to guess, and if a board seems to require guessing, either you have missed a deduction or the puzzle is badly made. Every board on this site is checked for a unique solution before you see it.

Where to start on a blank-looking grid

The first move is always the same: find the digit that already appears most often. If there are six 4s on the board, the 4 is heavily constrained — only three are missing, and the six you have rule out huge parts of the grid.

Take a box that is missing that digit. Every row already containing it is out. Every column already containing it is out. Cross those off and see what is left in the box. Often it is one cell, and you have solved it without considering a single other digit.

This is scanning, sometimes called cross-hatching, and it is how most of any easy puzzle gets filled in. Work one digit at a time across all nine boxes before moving to the next, rather than jumping around.

The last free cell

The other beginner move: any row, column or box with exactly one empty cell is free. The missing digit is whichever of 1 to 9 is not already there. It sounds trivial, and it is — but every digit you place creates new nearly-complete units, so a single placement often cascades into three or four more.

Between scanning and last-free-cell, a genuinely easy Sudoku will usually fall apart entirely. When it stops, you need the next question.

A worked example

Here is a real position where scanning has stopped producing anything obvious. Step through it — this is the move that gets you unstuck, and it is the one technique worth learning before any other.

What to learn next

That move is a hidden single, and with scanning it will carry you through most easy and medium boards. When it runs out — and on hard grids it will — the next step is to write candidates into cells and start eliminating rather than placing.

There is a short ladder of techniques beyond that, but it really is short. Four techniques cover essentially every puzzle you will meet.

Habits worth building early

• Never guess. Not on principle — because it does not work. A wrong digit propagates quietly and you find out twenty cells later, with no way back to where it went wrong.
• Use pencil marks once boards get hard. Every technique past hidden singles is defined in terms of candidates. Working without them past a certain difficulty is not purity, it is just harder.
• Finish a thought before starting another. The most common way to lose time is to spot something interesting three boxes away and abandon a deduction half-finished.
• When stuck, change the question. If “what goes in this cell?” has stopped working, switch to “where does this digit go in this unit?” They find completely different things.

Ready to play

There is a free 9×9 board on the home page with four difficulties, pencil marks and undo — start on easy and use scanning until it stops working. The daily puzzle gives you one fresh board a day, the same one everybody else is solving.