Naked singles
A naked single is an empty Sudoku cell with exactly one remaining candidate. Once the other eight digits are excluded by valid constraints or deductions, place the surviving digit. The proof concerns one cell, even when its row still has several empty spaces.
The worked example
Coordinates start at the top left: r = row, c = column. Small digits are candidates; outlined cells are discussed below.
Check this exampleView puzzle text
Read left to right across each row, then top to bottom. A 0 means a blank.
023406789056789123789123456234567891567891234891234567345678912678912345912345678Prove r1c1 = 1
The top row has two blanks: r1c1 and r1c5. This is not a last-cell-in-the-row shortcut. The row alone leaves two choices, so check the other units before committing.
| Unit containing r1c1 | Digits missing from that unit |
|---|---|
| Row 1 | 1, 5 |
| Column 1 | 1, 4 |
| Top-left box | 1, 4 |
Step 1. Row 1 permits only 1 or 5 in r1c1.
Step 2. Column 1 already contains 5 at r5c1, so remove 5 from consideration.
Step 3. The top-left box contains no 1, and neither does row 1 or column 1. The remaining digit 1 is legal in all three units.
Step 4. Place 1 in r1c1. No choice or trial branch was required.
Follow the effect of one placement
A correct move changes the candidate lists of its peers: cells sharing its row, column or box. Recheck those cells first instead of starting a fresh scan of the entire board. Here r1c5 is the only remaining blank in row 1, so it must be 5. Row 2 is missing only 4, which finishes r2c1.
This teaching example keeps most cells filled to focus on one deduction. It is not a difficulty-rated puzzle.
Naked single or hidden single?
The names describe the evidence you inspect. A naked single asks how many candidates remain in one cell. A hidden single asks how many positions remain for one digit within a row, column or box. A placement can satisfy both descriptions, but you only need one sound proof.
| Technique | What to count | When to place |
|---|---|---|
| Naked single | Candidates in one cell | Only one candidate remains |
| Hidden single | Legal cells for one digit in a unit | Only one position remains |
Check your notes
One pencil mark on the page does not automatically make a naked single. You may have forgotten to write another legal digit, or removed a candidate because of an earlier guess. Recalculate the row, column and box when a result looks suspicious.
If an empty cell has zero candidates, stop. That is a contradiction, not a more powerful single. Check copied givens and undo unproven entries before making more placements. A solver’s no-solution result is a different diagnosis from being unable to spot the next logical move.
Check your understanding
Why can r1c1 not be 5, even though row 1 is missing 5?
Show the reasoning
There is already a 5 at r5c1 in the same column. A digit must satisfy all three units simultaneously. Being absent from the row is necessary but not sufficient.
About this example
This teaching board keeps many givens to make the deduction clear and has no difficulty rating. Diagnosis examples deliberately include the stated conflicts or ambiguity.
Rules and terminology
- Nikoli: Sudoku rules
The standard row, column and 3 × 3 box rules used in these examples. The board and worked explanation on this page were created separately.
- Andrew Stuart: Naked Candidates
Established terminology for naked singles and their relationship to hidden singles. The board and worked explanation on this page were created separately.