Start from the cell
Most scanning starts from a digit and asks where it can go. A naked single turns the question round. You start from one empty cell and ask which digits it can still take.
Every cell has 20 peers: eight more in its row, eight more in its column, and four more in its box that are in neither. Cross off each digit that appears among them. If eight digits are crossed off, the cell is solved.
A worked example
This is the starting position of a daily puzzle. Look at the marked cell in row 2, column 3.
Its row holds 4, 3, 5, 2 and 7. Its column adds 8 and 6. Its box adds 1. Together that makes 1, 2, 3, 4, 5, 6, 7 and 8. The only digit not on the list is 9, so the cell is a 9.
Notice that no single unit settles it. The row alone leaves four possibilities and the box alone leaves four. It takes all three together.
A second one in the same grid
The same position has another, in row 7, column 7. The row holds 3, 8, 2 and 6. The column holds 5, 4 and 1. The box adds 9. The missing digit is 7.
This one is harder to see, because the row and column are each only half full. Cells like it are the reason naked singles get overlooked.
How to spot them
Checking all 20 peers of every empty cell is slow, so look where the odds are best: a cell at the crossing of a busy row and a busy column, especially inside a box that is more than half full.
Count upward rather than hunting. Say “one” and look for a 1 among the cell’s peers, then “two”, and so on. The first digit you can’t find is a candidate. If you reach nine with only one digit missing, place it.
If you take full notes, naked singles find themselves: any cell with a single note is one.
Common mistakes
- Forgetting the box. Four of a cell’s peers are in its box and in neither its row nor its column.
- Stopping at seven digits. Two missing digits is a pair of candidates, and it settles nothing yet.
- Trusting stale notes. If a note was not erased when its digit was placed nearby, a real naked single looks like a cell with two candidates.
A naked single’s mirror image is the hidden single, which starts from a digit and finds its only cell. Easy puzzles need both. On the six-by-six grid of Mini Sudoku, where a cell has only six possible digits, naked singles are far more common.