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TechniquesIntermediate

Naked Pair

Learn what a Naked Pair is in Sudoku, how to spot one, and how it eliminates candidates from a row, column, or box.

A Naked Pair occurs when two unsolved cells in the same unit are restricted to exactly the same two candidates.

Example:

  • r8c3 {3,9}
  • r8c4 {3,9}

Those two cells must contain 3 and 9 in some order.

You do not know which cell is 3 and which is 9.

But you do know that no other cell in the shared unit can be 3 or 9.

That reservation creates the eliminations.

Quick rule

Two cells.

Two candidates total.

Same row, column, or box.

→ Remove those two digits from other cells in the shared unit.

Why the pair is logically forced

A unit must eventually contain each missing digit exactly once.

The two pair cells have only two available values between them.

If one cell becomes 3, the other must become 9.

If one becomes 9, the other must become 3.

Either way, the pair consumes both digits.

So those digits are already reserved for the pair before their exact order is known.

This reservation idea is the foundation of Naked Subsets.

Step-by-step example

The pair can exist in any unit

The same logic works in:

  • a row;
  • a column;
  • a box.

A Locked Pair can eliminate in two units

Sometimes both pair cells share:

  • a row and a box;
  • or a column and a box.

Then the same two-digit reservation is valid in both units.

Example:

Two {2,7} cells sit in row 3 and box 3.

Candidate 2 and 7 may be removable:

  • elsewhere in row 3;
  • elsewhere in box 3.

This is often called a Locked Pair.

You do not need a separate solving rule. It is simply a Naked Pair whose cells share two units.

What is not a Naked Pair?

Consider:

  • {2,7}
  • {2,8}

Both cells are bivalue.

They share candidate 2.

But together they contain three distinct digits:

{2,7,8}

Two cells cannot reserve three digits.

So this is not a Naked Pair.

The useful test is:

Does the union of candidates across these two cells contain exactly two digits?

For a valid two-cell Naked Pair, the answer is yes.

Naked Pair vs Hidden Pair

Both describe a two-digits-for-two-cells reservation.

They are discovered from opposite directions.

Naked Pair

Look at the cells.

These two cells contain only digits 3 and 9.

Remove 3 and 9 from other cells.

Hidden Pair

Look at the digits.

Digits 3 and 9 appear only in these two cells.

Remove other candidates from the pair cells.

After a Hidden Pair is cleaned, it often becomes visually identical to a Naked Pair.

Naked Pair vs two bivalue cells in different units

The cells must share a unit.

Two {3,9} cells on opposite sides of the grid do not reserve 3 and 9 globally.

Sudoku restrictions operate through rows, columns, and boxes.

Always identify the unit that makes the reservation valid.

How to find Naked Pairs

With candidates visible:

  1. Choose one row, column, or box.
  2. Notice cells with exactly two candidates.
  3. Compare their candidate sets.
  4. Look for repeated pairs such as 27 ... 27.
  5. Confirm the cells share the unit you are inspecting.
  6. Search the rest of that unit for eliminations.

This is a cell-first technique.

Why Naked Pairs are an important milestone

Singles ask:

Which value is forced?

Naked Pairs introduce a new kind of certainty:

Which values are reserved, even though their exact cells are unresolved?

That same idea scales to:

  • Naked Triples;
  • Naked Quads.

And the inverse perspective gives:

  • Hidden Pairs;
  • Hidden Triples;
  • Hidden Quads.

So learning Pairs is really learning the general logic of subsets.

What a good pair elimination can unlock

A pair may remove only one or two candidates and still be decisive.

Example:

Naked Pair {3,9}
↓
remove 9 from another cell
↓
that cell becomes {5}
↓
Naked Single 5
↓
new candidate updates

The pair's value is the information it frees elsewhere.

Common mistakes

Removing the pair digits from the pair cells

Those candidates are the reservation. Keep them.

Using cells that do not share a unit

The elimination is valid only inside a row, column, or box shared by the pair.

Calling any two bivalue cells a pair

The combined candidate set must contain exactly two digits.

Assuming the pair solves both cells

The exact order remains unknown.

Forgetting a second shared unit

If the two cells also share a box, check the box as well as the row/column.

Recognition drill

When candidates are shown, look for repeated bivalue signatures:

18 ... 18

27 ... 27

46 ... 46

Then ask:

What unit do these cells share, and where do those digits appear elsewhere in that unit?

FAQ

Must both Naked Pair cells contain the same two candidates?

For a two-cell Naked Pair, yes.

Must the cells be adjacent?

No.

Can one Naked Pair eliminate candidates in both a row and a box?

Yes, when the pair cells share both units.

Is a Naked Pair always useful?

Not necessarily. If the pair digits do not appear elsewhere in the shared unit, the reservation creates no immediate elimination.

What to learn next

Learn Hidden Pairs to see the same reservation from the digit-first direction.

Then expand the subset idea to Naked Triples.

techniques · intermediateHidden PairLearn how Hidden Pairs work when two digits are restricted to the same two cells, and remove the extra candidates hiding the pair.techniques · intermediateNaked TripleLearn the Naked Triple rule: three cells whose combined candidates contain exactly three digits, allowing eliminations elsewhere in the unit.fundamentals · beginnerSudoku CandidatesLearn what Sudoku candidates are, how to calculate possible digits for a cell, and why candidates unlock intermediate and advanced solving.strategies · intermediateIntermediate Sudoku StrategiesLearn how to progress beyond Singles using candidates, Locked Candidates, Pairs, Triples and a structured intermediate solving workflow.