A Sudoku naked single explained: why A7 must be 7
A good Sudoku move has a reason you can check. You do not need to guess when the rules leave a square with only one possible number.
That situation is called a naked single: one empty square, one remaining candidate. Let’s work through a real example.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| A | 1 | 6 | 3 | 2 | 5 | 4 | · | 8 | 9 |
| B | · | 5 | · | · | · | 9 | 4 | 6 | · |
| C | · | · | 9 | 7 | · | · | 3 | 5 | 2 |
| D | 7 | 3 | 1 | · | · | 8 | 9 | · | 5 |
| E | · | · | 6 | 1 | 2 | · | 8 | 7 | · |
| F | 5 | 2 | 8 | 9 | 7 | 3 | 1 | 4 | 6 |
| G | · | 1 | · | · | 9 | · | 2 | · | · |
| H | 9 | 7 | · | 8 | 3 | · | 5 | 1 | 4 |
| I | · | 8 | · | 4 | 1 | 2 | 6 | · | 7 |
Find A7 on the board
For this 9×9 puzzle, rows A–I run from top to bottom, and columns 1–9 run from left to right. A7 is the square in the top row, seventh column. It belongs to the top-right 3×3 box.
Here is row A:
1 6 3 2 5 4 _ 8 9
The blank is A7. Every completed row must contain each number from 1 to 9 exactly once.
What is missing from the row?
Read the entered numbers carefully: 1, 6, 3, 2, 5, 4, 8, 9. Together, they include every number except 7.
So the row rule leaves only 7 for A7. There is no need to choose between several numbers, and no need to copy an answer from a solved board.
Before placing it, confirm that 7 does not conflict with the other two constraints.
Check the column
Column 7, from row A to row I, is:
_ 4 3 9 8 1 2 5 6
It already contains the other eight numbers and does not contain 7. Placing 7 in A7 is allowed by the column rule.
Check the box
The top-right box is:
_ 8 9 4 6 _ 3 5 2
Its missing numbers are 1 and 7. The box therefore allows 7 at A7 too.
The three checks agree: the row permits only 7; the column permits only 7; and the box permits 1 or 7. Their shared candidate is 7.
Now make the move
Select A7 and enter 7 as a full-size number, rather than leaving it as a pencil note. You have a checked placement: every alternative is excluded, and 7 breaks no row, column or box rule.
Afterwards, review notes in the affected row, column and box. Any 7 notes that now conflict with the placement should be removed. Squares elsewhere on the board are not affected just because they contain a 7 note.
What makes this a naked single?
The conclusion belongs to this square’s candidate list: A7 has exactly one candidate. That differs from a hidden single, where a number has only one available position within a row, column or box, even though that square may contain several notes.
If a square has candidates 2 and 8, you have not found a naked single. Keep both possibilities until another valid deduction removes one.
Try the method yourself
Find an empty square and check which numbers its row, column and box still allow:
https://smartpuzzles.github.io/play/sudoku/
The browser starter edition may resume your saved game rather than open this exact example. Look for the same pattern: one square with one candidate.
For native app features and Coach access details, see Smart Sudoku:
https://smartpuzzles.github.io/sudoku/