Naked Single

If a cell's row, column and box already hold eight different digits, the ninth is its answer.

Level: Elementary · technique 3 of 7

When to use it

Where a hidden single asks about a digit, a naked single asks about a cell. Look at crowded intersections: a cell whose row, column and box are all well filled.

If you keep pencil marks, it is simply a cell with one candidate left. Without pencil marks it takes the habit of crossing off 1 to 9 for the cell.

How to find it

1. Pick an empty cell with many digits around it.
2. Cross off every digit in its row.
3. Do the same for its column and its box.
4. If exactly one of 1 to 9 is left, that is the answer.

Worked example

On the board below, work out which digit goes in r7c8.

1. Look at row 7, column 8 and box 9 together - the three units r7c8 belongs to.
2. Between them they already hold 1, 2, 3, 5, 6, 7, 8, 9.
3. The only digit from 1 to 9 that is missing is 4, so r7c8 is 4.

Common mistakes

• Forgetting the box and checking only the row and column is the most common slip.
• A digit that is in both the row and the box counts once. Counting it twice makes the remaining set look smaller than it is.
• If more than one digit is left, this technique cannot decide the cell. Move to another cell or another technique.