Techniques · 1 of 10

The naked single

A cell with nowhere to hide. The most direct technique in Sudoku, and the one you will use most often.

A naked single is a cell where eight of the nine digits have already been eliminated by what sits in its row, column, and box — leaving exactly one possibility. The digit, in other words, has nowhere to hide; if you look at the cell carefully, it announces itself. There is nothing clever to spot. There is only the willingness to look.

The smallest possible example

Consider a board where one row is almost finished. Eight of the nine cells in row five already hold the digits 1, 2, 3, 4, 6, 7, 8, and 9. Only one cell — the fifth from the left — is empty:

The highlighted cell. Eight of the nine digits already live in this row; only 5 is missing.

The first row rule says the row must contain each of 1 through 9 exactly once. Eight of those digits are already placed. The ninth — the digit 5 — must therefore occupy the empty cell. There is no other possibility. The cell, in the language of solvers, is a naked single, and 5 is its only candidate.

That is the entire technique. You will see it at this level of clarity perhaps two or three times in an easy puzzle. Most of the time the picture is messier — the row has, say, five digits placed; the column adds two more digits; the box contributes one more; and between them they cover eight of the nine possibilities for that cell. The arithmetic is the same. The conclusion is the same.

How to find them

Three habits help:

1. Scan the densest rows, columns, and boxes first. A row with seven givens is far more likely to contain a naked single than a row with three. Walk the board, starting at whichever line is closest to being filled.
2. Combine row, column, and box. A cell sits at the intersection of three regions. The candidates left for the cell are exactly the digits absent from all three. When the three regions together cover eight digits, the ninth is forced.
3. Trust the simple deduction. Solvers often skim past naked singles looking for something cleverer — and then waste minutes circling back. If you have noted a cell with a single candidate, place it. Do not save it for later.

Naked singles and pencil notes

On Very Sudoku — and on any modern Sudoku grid — you can leave pencil notes in a cell: small candidate digits noting what is still legal. A naked single is the moment a cell's pencil notes have collapsed to a single candidate. If you have been writing notes, the technique becomes mechanical: any cell whose note string contains a single digit belongs to that digit.

Pencil notes also let you see naked singles forming. As you place new givens, candidates disappear from neighbouring cells. Sometimes a cell that began with four candidates loses three of them in one quick sweep — and is suddenly a naked single. Watch for cells that go quiet.

Why this technique sits at the foundation

Every other Sudoku technique exists to create a naked single (or its cousin, the hidden single). A naked pair, a pointing line, an X-Wing — none of them place a digit by themselves. They erase candidates. The erased candidates eventually leave some cell with only one possibility, and that cell is filled, which erases more candidates, which produces more singles. Sudoku, from this angle, is the repeated production of naked singles.

That is why intermediate solvers sometimes describe the experience of completing a hard puzzle as a cascade: nothing happens for a long while, then a chain of singles falls in sequence and a whole quadrant clears in a minute. The cleverness was in the setup. The finishing is naked singles.