How to play
sudoku.

Sudoku has three rules and one skill. The rules take a minute to learn. The skill, systematic elimination, takes a few puzzles to get comfortable with and a few weeks to make automatic. This guide covers both, in the order a beginner needs them.

The rules

The grid is nine by nine, divided into nine three-by-three boxes. Some cells are already filled. Your job is to fill the rest so that:

1. Every row contains the digits 1 to 9 once each.
2. Every column contains the digits 1 to 9 once each.
3. Every three-by-three box contains the digits 1 to 9 once each.

That is all. There is no arithmetic. A correctly made puzzle has exactly one solution and can be reached by logic alone, without guessing.

How to start: scan for forced digits

Pick a digit that already appears several times in the grid, say 7. Look at each box that does not yet have a 7. Cross out every cell in that box that shares a row or column with an existing 7. Often only one cell in the box remains. Write the 7 there. Repeat for the next box, then the next digit. This technique, called cross-hatching, solves most easy puzzles on its own.

A second opening move: find a row, column or box with only two or three empty cells. Work out which digits are missing and see which of them is blocked from all but one cell by the rest of the grid.

When scanning stalls: pencil marks

Harder puzzles reach a point where no single cell is forced. Now write small candidate digits in the empty cells: every digit that could legally go there given the current row, column and box. Two patterns then appear.

• Naked single. A cell has only one candidate left. Fill it in and remove that digit from the candidates in its row, column and box.
• Hidden single. A digit appears as a candidate in only one cell of a row, column or box, even though that cell has other candidates too. The digit must go there.

Alternate between the two until the grid moves again. Most medium puzzles fall to singles alone.

Two intermediate techniques

• Naked pair. Two cells in the same unit both have exactly the same two candidates, such as {3, 8}. Those two digits must occupy those two cells, so remove 3 and 8 from every other cell in that unit.
• Pointing pair. Within a box, a digit’s only candidates lie in a single row or column. The digit must be in that row or column inside the box, so remove it from the rest of that row or column outside the box.

With singles, naked pairs and pointing pairs you can finish almost every puzzle labelled easy, medium or hard in a newspaper. Techniques with names like X-Wing and Swordfish exist for expert grids; you do not need them to enjoy the game.

Habits that make you faster

• Scan one digit at a time across the whole grid rather than one cell at a time.
• Fill in a digit, then immediately check what it unlocks in its row, column and box.
• Keep pencil marks tidy and update them every time you place a digit; stale candidates cause most errors.
• If you find a contradiction, do not erase everything. Work back to the last confident placement.

Choosing puzzles

Start with puzzles marked easy or gentle until cross-hatching feels automatic, then move up one level at a time. Newspapers and their websites publish a free daily sudoku, usually rising in difficulty through the week. If you want the same daily rhythm with more variety and less time, Brisk’s brain teaser of the day serves two short number-pattern puzzles inside a two-minute challenge. For what sudoku does and does not do for your thinking, read does sudoku help your brain?