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A Naked Pair is a two-cell Naked Subset.
Two unsolved cells in the same row, column, or box are restricted to the same two candidates, such as:
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 know that the pair consumes both digits inside the shared house.
Therefore 3 and 9 can be removed from every other cell in that house.
Naked Pair at a glance
Two cells.
Two candidate digits in total.
One shared row, column, or box.
→ The two digits are reserved for the two cells.
→ Remove those digits from other cells in the shared house.
Schematic unit view — crossed candidates are the logical eliminations.
- Source candidates
- Eliminations
Why a Naked Pair is logically forced
A house must eventually place each missing digit exactly once.
If two unsolved cells can contain only 3 or 9, then there are only two possible assignments:
A = 3, B = 9
or
A = 9, B = 3Either way, those two cells use both 3 and 9.
No third cell in the same house can therefore contain either digit.
The exact order is unresolved, but the set of values is fixed.
This is the core idea behind all Naked Subsets.
Step-by-step row example
When verifying a Naked Pair:
- choose one house;
- identify the two candidate sets;
- confirm that the two cells are both restricted to the same pair of digits;
- keep those candidates in the pair cells;
- remove the pair digits from other cells in the house;
- re-scan the affected cells.
Naked Pairs work in rows, columns, and boxes
The proof depends on a shared house, not on its shape.
A Naked Pair can exist in:
- a row;
- a column;
- a 3×3 box.
The two cells do not need to be adjacent.
What does “naked” mean?
The pair is called naked because the reservation is visible directly in the candidate sets of the cells.
You look at the cells and see:
these two cells contain only X and Y.
That cell-first viewpoint contrasts with a Hidden Pair, where the important fact is that two digits have only two possible positions in the house even though the target cells contain extra candidates.
The candidate-union test
A useful general test for Naked Subsets is:
How many cells are in the set, and how many distinct candidate digits appear across those cells?
For a practical two-cell Naked Pair:
- cells = 2;
- distinct candidates across the pair = 2.
For example:
{2,7} + {2,7}
→ union {2,7}
→ 2 cells / 2 digits
→ Naked PairBut:
{2,7} + {2,8}
→ union {2,7,8}
→ 2 cells / 3 digits
→ not a Naked PairTwo cells cannot reserve three different digits.
Why you should solve Singles first
If one of the two cells has only one candidate, it is already a Naked Single and should normally be solved before searching for Pairs.
That is why Naked Pairs are usually presented as two bivalue cells containing the same two candidates.
The broader subset principle is about N cells restricted to N digits, but the simplest useful two-cell case appears after Singles have been exhausted.
Locked Pair: one pair, two shared houses
Sometimes the two pair cells share more than one house.
For example, two {2,7} cells may lie in:
- the same row;
- and the same box.
Then the reservation is valid in both houses.
Candidate 2 and 7 may be removable:
- elsewhere in the row;
- elsewhere in the box.
This configuration is often called a Locked Pair.
It does not require a separate logical rule. It is a Naked Pair whose two cells happen to share two houses.
Naked Pair vs Hidden Pair
Both techniques express the same two-digits-for-two-cells reservation from opposite directions.
Naked Pair — cell-first
These two cells contain only 3 and 9.
Remove 3 and 9 from other cells in the house.
Hidden Pair — digit-first
Digits 3 and 9 can appear only in these two cells.
Remove other candidates from the pair cells.
After a Hidden Pair is cleaned, the two cells often look exactly like a Naked Pair.
Naked Pair vs two unrelated bivalue cells
Two cells containing {3,9} do not form a global pair just because the notes match.
They must share at least one house.
Sudoku constraints act through rows, columns, and boxes. The reservation is valid only inside a house that contains both cells.
Always name the source house before making the elimination.
How to find Naked Pairs
Naked Pairs are naturally cell-first.
1. Choose one house
Inspect one row, column, or box at a time.
2. Notice bivalue cells
Cells with exactly two candidates are the easiest pair candidates.
3. Compare candidate signatures
Look for repeated sets such as:
18 ... 18;27 ... 27;46 ... 46.
4. Confirm the shared house
The pair must exist inside the row, column, or box you are using as the proof.
5. Search for eliminations
Remove the pair digits only from other cells in that house.
6. Check a second shared house
If both cells also share a box, row, or column, the same reservation may eliminate candidates there too.
Why Naked Pairs are an important milestone
Singles prove an exact value:
this cell must be X.
Naked Pairs introduce a broader kind of certainty:
these two cells must contain X and Y, although the order is unknown.
That reservation principle scales directly to:
- Naked Triples;
- Naked Quads.
The inverse positional viewpoint gives:
- Hidden Pairs;
- Hidden Triples;
- Hidden Quads.
Learning Naked Pairs is therefore really learning the foundation of the subset family.
A pair does not have to solve a cell immediately
The direct action is usually candidate elimination.
Naked Pair {3,9}
↓
remove 9 from another cell
↓
that cell becomes {5}
↓
Naked Single 5
↓
update peersA pair can be decisive even if it removes only one candidate.
Productive pair vs true-but-useless pair
Two cells may form a valid Naked Pair even when neither pair digit appears anywhere else in the shared house.
The reservation is still logically true, but there is no immediate elimination.
When solving manually, prioritize pairs that actually simplify another cell.
Common mistakes
Removing the pair digits from the pair cells
Those candidates are the reservation. Keep them.
Using cells that do not share a house
Matching notes alone are not enough.
Calling any two bivalue cells a pair
The candidate sets must reserve exactly two digits across the two cells.
Using {2,7} and {2,8} as a pair
Their union contains three digits, so no two-digit reservation exists.
Assuming the pair solves both cells
The pair fixes the set of values, not their order.
Forgetting a second shared house
A Locked Pair can create eliminations in both houses the cells share.
Recognition drill
When candidates are visible, scan one house and look for duplicated bivalue signatures.
Then ask:
“What two digits are reserved, what two cells reserve them, and in which house is the reservation valid?”
If you can answer all three parts, the eliminations become straightforward.
FAQ
Must both Naked Pair cells contain the same two candidates?
In the standard practical two-cell Naked Pair, yes: both unresolved cells are the same bivalue set after simpler Singles have been resolved.
Must the cells be adjacent?
No. They only need to share the house used by the deduction.
What is a Locked Pair?
It is a Naked Pair whose two cells share two houses, such as the same row and the same box. The pair can potentially eliminate its digits from both houses.
Can one Naked Pair eliminate candidates in both a row and a box?
Yes, when both pair cells belong to both units.
Is a Naked Pair always useful?
No. The pair can be valid without having another candidate to eliminate.
Is a Naked Pair a type of subset?
Yes. It is the two-cell form of a Naked Subset: two cells are restricted to two digits.
What to learn next
Learn Hidden Pairs to see the same two-for-two reservation from the digit-first direction.
Then expand the subset principle to Naked Triples and Hidden Triples.