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Naked Single

Learn what a Naked Single is in Sudoku, why one remaining legal candidate forces a placement, and how to find it with or without notes.

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A Naked Single is an unsolved cell with exactly one legal candidate remaining.

The proof is completely cell-first:

What can go in this cell?

If every digit except 8 is blocked by the cell's row, column, or box, then the cell must be 8.

There is no choice between alternatives because no alternative remains.

Sudoku visualA Naked Single has one legal candidate leftThe cell is solved from its own candidate set: every other digit has already been ruled out.
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  • Target cell
  • Candidates

Why is it called a Naked Single?

The word single means there is one forced possibility.

The word naked means that the possibility is exposed directly by the cell's candidate set rather than hidden among other candidates.

A cell written as:

{8}

is a Naked Single.

By contrast, a cell written as:

{2, 6, 9}

could still contain a Hidden Single if, for example, 6 has no other possible position in the relevant row, column, or box.

The names therefore describe two different ways a placement can be forced.

How a Naked Single works

For one unsolved cell, begin with the digits 1–9.

Remove any digit already present in:

  • the same row;
  • the same column;
  • the same 3×3 box.

The digits that survive are the cell's legal candidates.

If exactly one candidate survives, place it.

For example, if the peers of r6c7 contain every digit except 6, then:

r6c7 {6}

and therefore:

r6c7 = 6

The proof depends only on the constraints affecting that cell. You do not need to compare where 6 can appear elsewhere in the row or box.

Step-by-step Naked Single example

When reading a Naked Single example, verify the proof in a fixed order:

  1. check the row;
  2. check the column;
  3. check the box;
  4. combine the blocked digits;
  5. confirm that exactly one digit remains legal.

This matters because a digit blocked in only two of the three houses may still be legal in the cell.

How to spot Naked Singles with pencil marks

With complete candidates visible, Naked Singles are easy to recognise: look for cells containing exactly one note.

For example:

  • r4c2 {7} → place 7;
  • r8c9 {3} → place 3.

After the placement, remove that digit from all unsolved peers and re-scan. The update may create another one-candidate cell immediately.

This is why digital Sudoku with automatic candidates can make Naked Singles feel almost trivial: the candidate calculation has already been done for you, so recognition becomes the main task.

How to find Naked Singles without pencil marks

You do not need written candidates to prove a Naked Single.

Choose a promising empty cell and inspect its peers.

A reliable manual process is:

  1. note the digits already present in the row;
  2. add the digits already present in the column;
  3. add the digits already present in the box;
  4. identify which digits from 1–9 are still absent from that combined set;
  5. if only one legal digit remains, place it.

Cells in dense parts of the grid are good targets because their peers already contain many distinct digits.

Without candidate notes, Naked Singles can actually be harder to recognise than Hidden Singles, even though the proof is simpler. The interface changes visibility, not logical strength.

Naked Single vs Full House / last missing digit

These are both direct placements, but the proof starts from a different object.

Full House / last missing digit

A row, column, or box has only one empty cell. The missing digit must fill that final position.

The reasoning is house-first.

Naked Single

One cell has only one legal candidate after combining its row, column, and box constraints.

The reasoning is cell-first.

A particular move may satisfy both descriptions. If a row has one empty cell and that cell also has one candidate, either proof reaches the same correct placement.

For teaching and analysis, use the shortest proof that actually explains why the move is forced.

Naked Single vs Hidden Single

These are the two fundamental candidate-based Single viewpoints.

Naked Single

This cell has one possible digit.

The candidate count of the target cell is exactly one.

Hidden Single

This digit has one possible cell in a row, column, or box.

The target cell may still contain several candidates.

Sudoku visualNaked and Hidden Singles answer different questions
Cell-firstWhat can go in this cell?

{8}

Digit-firstWhere can this digit go in this house?

6 → one position

The distinction becomes especially useful once full candidates are visible. A one-candidate cell is a Naked Single; a candidate that appears once within a house is a Hidden Single.

Why one Naked Single can create another

Singles often propagate.

Suppose one cell contains:

{4, 7}

and a peer is solved as 4.

Candidate 4 must be removed, leaving:

{7}

The cell has become a Naked Single.

Placing 7 can then remove 7 from its peers, perhaps reducing another cell to one candidate.

This cascade is one reason easy puzzles can suddenly solve quickly after one breakthrough.

Naked Singles after candidate eliminations

Naked Singles are not only an opening technique.

More advanced deductions frequently create them.

For example:

  1. a Naked Pair removes candidate 3 from a neighbouring cell;
  2. that cell changes from {3, 8} to {8};
  3. it becomes a Naked Single;
  4. placing 8 may unlock additional Singles elsewhere.

The correct habit is therefore:

after every elimination, scan again for Singles before searching for another advanced pattern.

Advanced techniques do not replace Singles; they often exist to create them.

Candidate accuracy matters

A Naked Single is only as reliable as the candidate information behind it.

If a note has not been removed after an earlier placement, you may fail to notice a real Single.

If a legal candidate was removed incorrectly, a cell may falsely appear to contain only one possibility.

Before placing a suspicious one-candidate cell, especially after manual note editing, verify the row, column, and box directly.

That direct legality check is quick and protects against stale or incorrect pencil marks.

Common Naked Single mistakes

Placing a digit because it looks likely

A Naked Single requires exactly one legal candidate. If two candidates remain, the technique does not solve the cell.

Forgetting the box

Checking only row and column is insufficient. The 3×3 box can block an otherwise plausible digit.

Trusting stale notes blindly

Candidate notes must change after placements and eliminations. Old notes can hide or fake Singles.

Confusing a Hidden Single with a Naked Single

If the cell has several candidates but one digit is unique in the house, the proof is Hidden Single logic.

Assuming every one-note display is automatically correct

If candidates were entered manually, verify the underlying constraints before treating the display as proof.

Tips for finding Naked Singles

  • With full notes visible, scan for one-candidate cells after every elimination.
  • Without notes, inspect cells whose peers contain many different digits.
  • Check the row, column, and box in a consistent order.
  • Re-scan the three houses affected by every placement.
  • If no Naked Single exists, switch to Hidden Singles or another family instead of trying to force the pattern.

FAQ

Is a Naked Single the easiest Sudoku technique?

It is one of the simplest logical deductions, especially when candidates are displayed. A Full House / last missing digit can be even more visually immediate because only one cell remains in the house.

Can a Naked Single have two candidates?

No. By definition, the cell has exactly one legal candidate remaining.

Do I need to write candidates to find a Naked Single?

No. You can derive the same result by checking which digits are blocked by the cell's row, column, and box. Written candidates simply make the result visible.

Is a Naked Single always safe to place?

Yes, if the candidate calculation is correct. With only one legal digit remaining, the placement is forced by the Sudoku constraints.

Can an advanced technique create a Naked Single?

Yes. Candidate eliminations from subsets, Fish, Wings, Chains, and many other techniques can reduce a cell to one remaining candidate.

What to learn next

Learn Hidden Singles next. Together, Naked and Hidden Singles teach the two fundamental candidate viewpoints: one possibility for a cell and one position for a digit inside a house.

Fundamentals · BeginnerSudoku CandidatesLearn what Sudoku candidates are, how to calculate possible digits, update candidate sets, and use candidates to recognize solving patterns.Techniques · BeginnerHidden SingleLearn what a Hidden Single is, how it differs from a Naked Single, and how to find a digit with only one legal position in a row, column or box.Techniques · BeginnerScanning in SudokuLearn how to scan Sudoku rows, columns, boxes, cells and digits systematically to find forced placements and useful restrictions.Strategies · BeginnerBeginner Sudoku StrategiesLearn beginner Sudoku strategies using last missing digits, scanning, Naked Singles, Hidden Singles, simple candidate notes and a repeatable solving order.
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