How to solve sudoku: techniques from easy to advanced

Every sudoku on this site can be solved by logic. Here are the techniques in the order you should look for them: simple ones first, and the harder ones only when the simple ones don't help.

Candidates and pencil marks

A cell's candidates are the digits that can still go there: they don't appear in the cell's row, column or box. On easy puzzles you can keep candidates in your head; on harder ones it's easier to write them down as notes. Use the Notes mode (N key) or "Fill in all notes" in the settings.

1. Naked single

A cell has only one candidate left: the other eight digits already appear in its row, column or box. Place that digit. This is the most common move on easy puzzles.

2. Hidden single

A digit has only one possible place in a row, column or box, even though the cell itself allows other digits. Example: a box has no 7, and every cell but one is blocked by 7s in neighbouring rows and columns. So the 7 goes in the remaining cell. Medium puzzles are built on this technique.

3. Pointing and claiming

If inside a box a digit can only be in one row (or column), it can't appear in the rest of that row outside the box — remove that candidate. It also works the other way: if in a row a digit can only be inside one box, remove it from the other cells of that box.

4. Naked pairs and triples

Two cells in the same row, column or box contain the same two candidates, for example {3, 8}. Then 3 and 8 must occupy exactly those two cells, so they can be removed from the other cells of the group. Three cells sharing three candidates — a triple — work the same way.

5. Hidden pairs and triples

Two digits can only go in the same two cells of a group. Then those cells can't contain anything else — remove their other candidates. Hidden pairs are harder to spot than naked ones: look at digits, not cells.

6. X-Wing

In two rows a digit can only go in the same two columns. This forms a rectangle: in those rows the digit occupies two opposite corners. Either way, each of the two columns gets the digit in one of these rows, so it can be removed from the other cells of those columns. It also works with rows and columns swapped.

7. XY-Wing

Three cells with two candidates each: a "pivot" {X, Y} and two "wings" {X, Z} and {Y, Z}, each seeing the pivot. However the pivot resolves, one of the wings will be Z. So Z can be removed from every cell that sees both wings.

8. Swordfish

X-Wing extended to three rows and three columns: in three rows a digit can only go in the same three columns. Then it can be removed from the other cells of those columns.

General tips

• Always look for simple moves first: one single often unlocks a whole chain of others.
• Update your notes after every new digit — the site does this automatically.
• Don't guess: if it seems there are no moves, you have probably missed a hidden single or a pair.

Practice on any level: easy, medium, hard and expert sudoku.