Naked single
When a cell's row, column and box already hold eight different digits, the ninth is the only one left.
The idea
Take one empty cell and collect the digits it can see: those in its row, its column and its box. If eight different digits appear, the missing one is the only candidate for the cell.
With pencil marks this is the easiest technique to see: a cell with a single candidate. Without them you have to count, which is why hidden singles are often found first.
How to spot it
- Look at cells in crowded areas: where a full-looking row crosses a full-looking column.
- If you keep notes, any cell with one note left is a naked single.
- The last empty cell of a row, column or box is the simplest case of all.
Worked example
Naked single on a real puzzle
From our easy puzzle #6 (36 clues), after 18 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out, green is the digit it places.
How often our puzzles need it
Our solver works like a careful player: it always uses the easiest technique that still makes progress. Counting the puzzles where it had to use naked single at least once:
- 42 of our 1000 easy puzzles
- 602 of our 1000 medium puzzles
- 960 of our 1000 hard puzzles
- 930 of our 1000 expert puzzles
- 938 of our 1000 master puzzles
The easiest level that can need it is easy Sudoku.