Lesson 3 of 7 · Core technique
Naked singles: the only digit that fits
The guide and all sudoku lessons
Scanning asks where a digit can go. A naked single asks the opposite question about one square: what can it hold? Look at everything the square can see, its row, its column and its box, and cross off every digit already there. When exactly one digit is left, that digit is the answer.
It is called naked because the answer is out in the open once you have looked: the square has a single candidate. The last empty square is the simplest case, where one unit, a single row, column or box, does all the work. The more useful naked singles need all three units together.
Example 1: Row, column and box together
Step 1 of 6
Take the empty square at row 7, column 5. What could it hold?
Take the empty square at row 7, column 5. Its row rules out six digits: 1, 2, 3, 4, 5 and 7. Its column adds the 9, and its box adds the 6. That is eight different digits, so the square can only be an 8.
No single unit was enough here: the row alone still leaves three candidates.
Example 2: When the box does most of the work
Step 1 of 6
Row 4, column 8 is empty. What could it hold?
Row 4, column 8. Its row has only four digits, 2, 4, 7 and 9, which leaves five candidates. Its column adds the 3. Its box then adds 5, 6 and 8 at once, and only the 1 is left.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
What digit goes in the ringed square? Look at its row, its column and its box together.
Pick the digit for the ringed square.
How to spot it faster
- Look where the board is crowded. A square whose row, column and box are all well filled has the fewest candidates.
- Count what a square can see rather than guessing what it might be. Eight different digits in sight means a naked single.
- Once you keep notes, naked singles are the squares showing a single pencil mark, which is why accurate notes matter.
Common mistakes
Checking only one or two units
A square's candidates come from its row, its column and its box. Skip one and you will either see candidates that are not there or miss the digit that rules out the one you place.
Trusting stale notes
Pencil marks are only as good as the last time you updated them. Placing a digit clears it from every square that can see it, but no deduction is applied for you: a mark a pair has ruled out stays until you remove it.
Confusing it with a hidden single
A naked single is one square with one candidate. A hidden single is one digit with one possible square. Both are safe placements, but you find them by looking at different things.
Questions
Try it
Pick an empty square in a crowded part of the board and count what it can see. When you find one with a single candidate, you have done it.
Play solo on an easy 9×9