The cell that has only one answer left

The short version

A naked single is an empty cell where eight of the nine digits have already been ruled out. The ninth is not a guess, not a likelihood, and not a hunch. It is the only value the cell can legally hold, so you fill it in and move on.

The reasoning is trivial. Finding them is the actual work, and that work is bookkeeping: unless the candidates are written down, a cell with one option looks exactly like a cell with four.

What makes it "naked"

The word is not decoration. In sudoku, a move is naked when the information sits inside the cell itself, and hidden when it only exists across the unit the cell belongs to.

A naked single is naked because the constraint is visible in that one square: you look at the cell, count what is left, and there is one number. You do not need to compare it with anything else on the board.

Why the placement is forced

Every row, every column and every 3×3 box must contain the digits 1 through 9 exactly once. Take any empty cell. If a digit already appears in its row, the cell cannot hold that digit. Same for its column. Same for its box.

So a cell's candidate list is simply 1–9 minus everything visible in those three units. When that subtraction leaves one digit, the cell has one legal value and no other.

There is a second, less pleasant consequence: if you ever reach a cell where no digit fits, you did not find a hard puzzle. You made an earlier mistake. The correct response is to undo, not to guess.

A real board

Here is a position taken from an actual game. Row 1, column 2 is the cell we care about.

Look at what surrounds it:

• Row 1 already holds 9, 1, 7 and 8.
• Column 2 adds 3, 4 and 2.
• The top-left box adds one more digit: 6.

Together that is 1, 2, 3, 4, 6, 7, 8 and 9 — eight distinct digits. One is missing. R1C2 is 5, and there is nothing to deliberate about.

Notice that no single unit was enough. The row rules out four digits and the column three more, which still leaves the cell with two candidates — 5 and 6. The box settles it. This is exactly why naked singles punish people who check only the row and the column: on this board, stopping after two units leaves you with a cell that looks like a coin flip.

The scanning routine

Naked singles cluster where the board is dense, so scanning at random wastes time. A workable order:

1. Finish a unit before leaving it. When you place a digit, its row, column and box each lose one candidate. Check those twenty cells immediately — that is where the next single usually appears.
2. Start with the emptiest-looking region. Cells surrounded by many filled neighbours have short candidate lists, and short lists are cheap to verify.
3. Count, do not list. You are not trying to enumerate candidates. You are asking one question: how many digits are still possible here? If the answer is one, fill it.
4. Prefer cells with four or fewer candidates. A cell showing six candidates will almost never be a naked single; skipping those is not laziness, it is triage.

On a well-maintained board this routine finds most naked singles in a couple of seconds each.

Where people lose minutes

Forgetting the box. By far the most common. Rows and columns are visually obvious; the box boundary is a thin line you stop seeing after ten minutes. Every naked single check is three units, not two.

Trusting pencil marks after a correction. If you erase an entry, the candidates it had blocked do not restore themselves. A wrong pencil mark turns a two-candidate cell into a fake single, and the mistake propagates quietly for several moves before the board contradicts itself.

Scanning cells when the puzzle wants digits. Naked singles are cell-shaped, hidden singles are digit-shaped. If the board feels stuck, switching scan direction often finds a move in seconds.

Naked single, hidden single, same placement

The two are easy to conflate because they frequently produce the same answer from different directions.

Neither is more advanced. A hidden single is often easier to see when you scan 1 through 9 systematically, and a naked single is easier to see when a cell has many filled neighbours. Good players alternate.

Naked singles also mark the end of the opening. Once every open cell is down to two or three candidates, cell-scanning stops paying — that is where digit-shaped work like the hidden pair takes over.