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.
You will also see this called the last possible number, or the sole candidate. Both names describe the same move from the other end — the result rather than the pattern — and there is no difference in the reasoning.
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.
Common questions
What is a naked single in Sudoku?
A naked single is a square whose candidate list has shrunk to one digit. Its row, column and box between them have ruled out the other eight, so the survivor is forced. It is the most direct placement in Sudoku.
What is the difference between a naked single and a hidden single?
A naked single is a fact about one square: only one digit still fits it. A hidden single is a fact about one unit: only one square in a row, column or box can take a given digit, even though that square may still accept other digits too. Naked looks at the square, hidden looks at the unit.
Do I need pencil marks to find naked singles?
In practice yes. A naked single is only visible when you are already tracking candidates, because otherwise you would have to re-derive a square's options every time you looked at it. Keeping notes current is what makes them appear on their own.
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.
Coming to this cold? The step before it is cross-hatching, and this technique is usually the one you reach for when that stops opening squares.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board. Run a puzzle site? Embed this board.
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