Naked singles

A naked single is a cell that can hold only one digit. Look at the row, the column and the box the cell belongs to: if eight different digits already appear among them, the ninth is the only one left, and it must go in that cell. It is called “naked” because the answer is plain to see once you look at the cell itself; nothing about the rest of the unit needs to be worked out.

Naked singles and hidden singles are the two basic moves of sudoku. Every puzzle uses them, and on easy puzzles they are all you need. Hidden singles ask “where can this digit go?”; naked singles ask the opposite question, “what can go in this cell?”. Good solvers switch between the two all the time.

Why it works

The rule of sudoku is that every row, column and box contains each digit exactly once. So a digit that already appears anywhere in a cell's row, column or box cannot go in that cell. Those three units together contain 20 other cells (the cell's “peers”). When the digits in the peers cover eight of the nine values, only one candidate survives. No other reasoning is needed and no guess is involved: the remaining digit is forced.

Naked singles become common in the second half of a puzzle, when rows and boxes are filling up. Early on, when the grid is mostly empty, few cells have eight different digits among their peers, which is why hidden singles usually get a puzzle started and naked singles finish it.

How to spot it

• Look for cells where the row, column and box are all crowded. A row with seven digits already placed is a good place to start.
• Count what is missing rather than what is present: if a row is missing only 3 and 8, check each empty cell’s column and box for a 3 or an 8.
• With pencil marks, a naked single is simply a cell with one note left. Keep notes up to date and they jump out.
• Use highlighting: selecting a cell shades its row, column and box, so you can read off the digits that are already used.

Common mistakes

• Forgetting the box. It is easy to check the row and column and miss a digit sitting in the same 3×3 box.
• Trusting stale notes. If you placed a digit and did not remove it from nearby notes, a cell may look like it has two candidates when it really has one (or the reverse). Turn on “Auto-remove notes” to avoid this.
• Placing a digit because it is the only one you can think of. A naked single is only forced when the other eight digits are all visibly ruled out; if you cannot point to each of them, it is a guess.

Related techniques

In pencil-mark terms, a naked single is the simplest member of a family. Two cells in a unit with the same two candidates form a naked pair; three cells with three candidates between them form a naked triple. Each one says the same thing: a group of cells has used up a group of digits. Learning to see naked singles quickly is the foundation for all of them.

Stuck on a real puzzle? The sudoku solver names every technique it uses, step by step, and the hint button in the game teaches the same way.

How to practise

Play the three practice puzzles below in order. Each one reaches a point where naked singles are the only way forward with the basic toolbox, so if you get stuck, that is the moment to look for the pattern. Try first without help. If you still cannot see a move, press Hint once: the first level names the technique, the second shows where to look, and only the third makes the move for you. After you finish, play a few easy puzzles without hints to make the habit stick.