How to solve sudoku: seven strategies, from easy to expert

The one rule behind every technique

Sudoku has a single rule: every row, every column and every 3×3 box must contain the digits 1 to 9 exactly once. Every solving technique, from the simplest to the most advanced, is just a clever way of applying that rule. A well-made sudoku always has exactly one solution and never needs guessing.

You can try each technique below in our free online sudoku, which has easy, medium, hard and expert levels and unlimited puzzles.

1. Scanning (cross-hatching)

Pick a digit, say 5. Look at every 5 already on the board. Each one rules out its whole row and its whole column. Now look at each 3×3 box that still needs a 5: if only one empty cell in that box is not ruled out, the 5 goes there.

Scanning is how most people start, and on easy sudoku it solves almost the whole grid.

2. Pencil marks

When scanning stops working, write the candidates: the small digits that could still go in each empty cell. It feels slow, but it turns sudoku from guesswork into logic. Every technique from here on depends on candidates.

3. Naked single

A cell whose candidates have been reduced to exactly one digit must be that digit. After you place it, remove that digit from the candidates of every cell in the same row, column and box, and look for new naked singles.

4. Hidden single

Sometimes a cell still has several candidates, but one of them appears nowhere else in its row, column or box. Then that cell must hold that digit, even though other candidates were written in it. Hidden singles are the most useful technique in medium puzzles, and the one beginners most often miss.

5. Naked pairs (and triples)

If two cells in the same unit (row, column or box) both have exactly the same two candidates, for example {3, 7}, then those two digits must go in those two cells. You can remove 3 and 7 from every other cell in that unit. The same idea works with three cells sharing three candidates.

6. Pointing pairs

Look inside one box. If all the candidates for a digit in that box lie in one row (or one column), then the digit must be in that row inside that box. So you can remove that digit from the rest of the row outside the box. This small technique unlocks many hard sudoku puzzles.

7. X-wing

The X-wing is the classic advanced technique. Find a digit that, in two different rows, can go in exactly two cells, and those cells sit in the same two columns. The digit must be in one diagonal pair of those four corners, so it cannot appear anywhere else in those two columns. Remove it there. You will need this and similar patterns on expert sudoku.

The order to use them

1. Scan every digit.
2. Fill in pencil marks.
3. Look for naked singles, then hidden singles. Repeat until stuck.
4. Look for naked pairs and pointing pairs.
5. Only then try X-wing and advanced patterns.

A worked example

Imagine the top-left box already holds 1, 2, 4, 6, 8 and 9, leaving three empty cells. The first row of the grid already contains a 3 further to the right, and the second column contains a 5 further down. Now look at where 3 can go inside the box: it cannot sit in the first row, so it must be in one of the other two cells. Then check where 5 can go: it cannot sit in the second column. If only one cell is left for 5, place it. That single deduction often starts a chain, because the new 5 rules out more cells in its row and column.

Common mistakes

• Guessing. A guess that seems to work can hide an error that only shows up ten moves later.
• Forgetting to update pencil marks after placing a digit.
• Only scanning rows. Columns and boxes hide just as many singles.

Keep practising

Sudoku skill grows fast with practice. Start with easy sudoku, move up level by level, and when classic sudoku feels comfortable, try killer sudoku, where cages with sums add a new layer of logic.