Sudoku technique

Naked Single

A cell only has one digit left: every other number is already placed somewhere on its row, column, or box. It’s the most direct deduction in sudoku — no need to check any neighboring candidates.

A puzzle that requires it

Level Beginner — the puzzle is shown twice: right below, and again in the demo that follows.

5		7	8	1	9	2	4	3
9	4	8		2	6		1
			4					8
3	5	2	6	8	4			9
1		4	5	9	3	8		6
6			1	7	2	4	3	5
7					1
	2		7	4		3	9	1
4	3	1	9	6	8	7		2

Demonstration

State of the grid right when the technique applies, after 0 earlier deductions.

Demo

Demo — watch first, you'll play right after.

Technique's pattern
Cell solved by the technique
Solved earlier
Given (clue)

5		7	8	1	9	2	4	3
9	4	8		2	6		1
			4					8
3	5	2	6	8	4			9
1		4	5	9	3	8		6
6			1	7	2	4	3	5
7					1
	2		7	4		3	9	1
4	3	1	9	6	8	7		2

Singleton nu

Dans la case surlignée, un seul chiffre est encore possible : regarde sa ligne, sa colonne et son carré.

Placement:

the 6 in L1C2

Your turn: puzzle 1 →

The Naked Single is the most direct deduction in sudoku: an empty cell has only one candidate left, so that digit is the one it holds. It is called “naked” because the digit stands alone in the cell, with no need to look anywhere else.

The principle

Every cell must receive a digit from 1 to 9. That digit cannot already appear in the cell’s row, in its column or in its box. If, taking those three zones together, eight different digits are already placed, only one remains for the cell. It cannot stay empty and it cannot hold any other digit, so the deduction is certain.

The reasoning assumes nothing about the rest of the grid. All it needs is that the eight excluded digits really are placed, whether you found them yourself or they were there from the start.

How to spot it

Pick an empty cell, preferably where a well-filled row and a well-filled column cross, or inside a box that is nearly complete. Read the digits in its row, then its column, then its box, counting each digit only once. A digit that sits in both the row and the box counts as one.

If you reach eight distinct digits, the ninth is the answer. If not, move on to another cell. With practice you start with the zones that are missing only one or two digits, because that is where Naked Singles cluster.

If you pencil in candidates, the search becomes visual: just look for a cell with a single candidate. After each digit you place, strike it from the notes of its row, its column and its box. That step is what makes the next singles appear.

A worked example

Take an empty cell whose row, column and box together contain, once duplicates are set aside, eight different digits. Only the ninth can go in the cell, so you place it. It does not matter whether those eight digits are spread evenly across the three zones or all sit in one of them: only their number counts.

The natural habit is to carry on right away. The digit you have just placed removes a candidate from every cell in its row, column and box. One of those cells sometimes has a single candidate left, and the grid unrolls step by step.

Common mistakes

The most common mistake is counting a digit twice. A digit that appears in the row and in the box rules out only one digit, which sometimes leaves two candidates where you thought you had one.

Another trap is mixing up row and column when reading quickly, or forgetting to check the box. One missed digit leads you to place a digit that is already in the zone, and the error only shows much later. Finally, if you keep notes, update them after every digit you place: a stale note makes you miss a single.

When to use it

The Naked Single is enough to solve Beginner puzzles, where every cell follows from simple elimination. It stays in use at every level after that, but Easy puzzles also ask for the next technique in the catalog, the Hidden Single.

When no cell has a single candidate left, change your point of view: instead of looking at a cell, look at a digit within a zone.

Frequently asked questions

What is the difference between a Naked Single and a Hidden Single?

In a Naked Single, one cell has only one candidate left. In a Hidden Single, one digit has only one possible cell in a zone, even if that cell still accepts other digits. The first is read cell by cell, the second digit by digit.

Do I need to pencil in candidates to find a Naked Single?

No. On easy puzzles, many players spot Naked Singles by reading the row, column and box of a cell. Notes become useful when many cells are still open: nothing gets lost from view.

Can a Naked Single be wrong?

Not if the starting grid is correct and every excluded digit is really placed. A wrong result means a mistake was made earlier: one misplaced digit throws off every deduction that depends on it.