How to Play Sudoku: Rules, Strategies and Tips for Beginners

Sudoku looks like a maths puzzle, but it contains no maths at all. You could swap the digits for nine colours or nine animal pictures and the game would play exactly the same. What it really tests is logic: every number you place is one you can prove belongs there. This guide covers the rules, a method for getting started on any grid, the techniques that move you from easy puzzles to hard ones, and the habits that stop a good solve going wrong near the end.

The rules of sudoku

A standard sudoku is a 9x9 grid divided into nine 3x3 boxes. Some squares start filled in; these are called givens, and you cannot change them. Your job is to fill every empty square with a digit from 1 to 9, following three rules at once.

• Each row must contain every digit from 1 to 9 exactly once.
• Each column must contain every digit from 1 to 9 exactly once.
• Each 3x3 box must contain every digit from 1 to 9 exactly once.

That is the whole game. A properly made puzzle has only one solution, which means guessing is never required. If you feel you have to guess, there is a logical step you have not spotted yet. You can try the rules right now in Easy Sudoku Puzzle, which offers hints and undo while you learn, or in Sudoku Master for a plain 9x9 grid.

How to start any sudoku puzzle

Beginners often stare at the empty squares and ask what could go there. It is faster to reverse the question: pick a digit and ask where it can go. Start with whichever digit already appears most often on the grid, because the more copies are placed, the fewer places remain for the rest.

Say five 7s are already placed. Look at a box with no 7. Follow each existing 7 along its row and column, and mentally cross out every square in that box those lines pass through. If only one empty square survives, the 7 goes there. This is called scanning or cross-hatching, and it solves most of an easy puzzle by itself. Work through every box for that digit, then move on to the next most common digit, and keep looping.

Techniques for medium and hard sudoku

When scanning stops producing answers, the puzzle has not become unfair. It simply needs a closer look. These techniques cover the great majority of puzzles you will meet, and each one is a way of proving where a digit cannot go.

• Naked single: a square where only one digit is still possible, once you check its row, column and box together.
• Hidden single: a square that may allow several digits, but one of those digits fits nowhere else in that row, column or box.
• Naked pair: two squares in one group that can only hold the same two digits. Those digits can be removed from every other square in the group.
• Pointing pair: when a digit in a box can only sit in one line of that box, it can be removed from the rest of that line outside the box.
• X-wing: a harder pattern where a digit is limited to the same two columns in two different rows, which removes it from those columns elsewhere.

Use pencil marks, but use them late

Pencil marks are small candidate notes written in a square. They are essential on hard puzzles, because techniques like pairs only become visible once the candidates are written down. Marking the whole grid at the very start, however, is slow and hides easy answers under clutter. Scan first, place everything you can, and only then note candidates for the squares that remain. Update the notes each time you place a digit, since one placement can remove candidates across a row, a column and a box.

Common sudoku mistakes

• Guessing and moving on. One wrong guess can sit unnoticed for twenty moves, and the error only appears when a row refuses to work.
• Checking only rows and columns. The 3x3 box is the rule people forget most, and it is often the one that gives the answer.
• Sticking with one digit for too long. If a number is going nowhere, switch. A placement elsewhere may unlock it.
• Ignoring a contradiction. If two squares both need the same digit, stop and use undo rather than pressing on.

How to get faster at sudoku

Speed comes from pattern recognition, not rushing. Solve easy grids until scanning feels automatic, and try to spot singles without moving your eyes square by square. Then move up one difficulty at a time. A short daily puzzle works better than an occasional long session, and it fits neatly into a coffee break. If you enjoy this style of thinking, our free brain games guide and the number games page are good next steps, and Math Sticks Puzzle offers a very different kind of number logic.

Sudoku difficulty levels

Difficulty has little to do with how many numbers are given at the start. What matters is which techniques the puzzle demands. An easy grid can be finished by scanning alone, a medium one usually needs candidates and pairs, and a hard one may need a pattern such as an X-wing. So if a puzzle with plenty of givens feels impossible, it may simply need a technique you have not learned yet.

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