Naked single
A naked single is the most direct move in Sudoku: a square where eight of the nine digits are already spoken for by its neighbours, so the ninth is forced. It is the deduction pencil marks exist to reveal.
The idea
Every square has twenty peers — the eight others in its row, the eight in its column, and the four remaining in its box that you have not already counted. If those peers between them show eight different digits, only one digit is left, and it belongs in that square.
It is called naked because there is nothing hidden about it. The candidate is sitting there on its own, visible the moment your notes are up to date.
A worked example
Count what r5c5 cannot be:
- Its row already holds 1, 2 and 3.
- Its column already holds 5 and 6.
- Its box already holds 7, 8 and 9.
That is eight distinct digits. Only 4 survives, so 4 goes in the centre — and it is worth noticing that no single unit did the work. Three different units each contributed, which is exactly why naked singles are easy to walk straight past when you are scanning one row at a time.
How to spot them
This is the technique that repays keeping notes. A square whose pencil marks have shrunk to one digit is a naked single by definition, so if your notes are current you do not hunt for these at all — you just notice them.
Without notes, the practical trick is to check squares in the most crowded regions of the board. A square sitting where a full row crosses a full column is the likeliest place for eight peers to have accumulated.
Common mistakes
Stale notes are the whole risk here. A pencil mark you forgot to erase after an earlier placement can hide a naked single indefinitely — the square shows two candidates, one of which is no longer possible. When a puzzle feels stuck for no reason, re-derive the notes in the region you are working on rather than trusting what is written.
The mirror error is erasing too eagerly and creating a naked single that is not really there. If a placement surprises you, count the eight peers explicitly before committing.
Where to go next
The next technique in the order is hidden single — The only square in a row, column or box that can hold a digit — even when it still shows other notes.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board.