How to solve Sudoku

Every valid Sudoku can be solved by reasoning alone. Guessing is never required, and knowing that changes how you play.

Sudoku has one rule: each digit from 1 to 9 appears once in every row, column and three-by-three box. Everything else follows from it.

The techniques, in the order they become useful

Scanning. Pick a digit and look at where it already appears. Its rows, columns and boxes are excluded, and often only one square in a box is left. This solves most easy puzzles entirely.

Naked singles. Look at a square rather than a digit. If eight of the nine digits appear in its row, column or box, the ninth belongs there.

Hidden singles. The most commonly missed. A square may have several candidates, but if a digit can go in only one square of a unit, it goes there regardless of what else that square could hold.

Pairs and triples. If two squares in a unit both hold exactly the same two candidates, those digits are used up between them and can be struck from every other square in the unit — even though you cannot yet say which is which.

Pointing pairs. If a digit's only places within a box all lie in one row, the digit is somewhere in that row inside the box, so it can be eliminated from the rest of the row.

X-wing. A digit confined to the same two columns in two separate rows can be removed from those columns elsewhere. This is where puzzles stop being routine.

What difficulty actually measures

Difficulty here is the hardest technique required, not the number of givens. That is a more honest measure: a puzzle with 28 clues solvable by scanning is easier than one with 32 that needs an X-wing. The generator solves each puzzle with the techniques in order and grades it by the furthest it had to reach.

Every puzzle is also checked to have exactly one solution. A puzzle with two is broken, however pleasant it looks, because it cannot be solved by reasoning — only by picking one and hoping.

Pencil marks

Noting candidates is not cheating, it is how the harder techniques become visible — you cannot spot a naked pair without seeing both squares' candidates. Keep them accurate; a stale mark left after an elimination is the usual source of a contradiction that appears from nowhere.

Frequently asked questions

Does every Sudoku have exactly one solution?

A properly constructed one does, and every puzzle here is verified to. A puzzle with more than one solution cannot be finished by reasoning alone, which most solvers would consider broken.

Is guessing ever necessary?

No. If you are stuck, either a technique you know applies somewhere you have not looked, or you have made an earlier mistake.

What does the difficulty rating mean?

The hardest technique needed to finish, not the number of starting digits. Clue count correlates only loosely with how hard a puzzle actually plays.