Overview
- Tier 3
- Subsets
- Typical difficulty
- Peak Score 30–45
- Also known as
- Disjoint Pair, Naked Twin, Pair Subset
When two cells within the same row, column, or box contain only the exact same two candidates {A, B}, those two digits are locked into those two cells and can be eliminated from all other cells in that house.
A Naked Pair is the simplest subset technique in Sudoku. If two cells in a house have candidate sets restricted strictly to {A, B}, one of them must be A and the other must be B. We don't yet know which is which, but we know with 100% certainty that neither A nor B can appear anywhere else in that common house.
Worked examples
1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates
7
149
3
49
145
6
1459
2
8
2
1489
568
3
145
7
14569
56
14
146
149
56
489
2
18
145679
3567
134
9
7
4
6
8
3
2
1
5
5
3
1
2
7
4
8
9
6
8
6
2
1
9
5
3
4
7
14
2
9
48
6
18
1457
357
134
146
148
7
5
3
9
146
68
2
3
5
68
7
14
2
146
68
9
In row 9, R9C3 and R9C8 hold only {6,8} between them. Those two cells must take those two digits, so 6 and 8 can be removed from the rest of row 9.
Removes: 6 from R9C7
How to apply it
Spotting the pattern and making the deduction, in order.
- Find two cells in the same row, column, or 3×3 box that each contain only the exact same two candidates (e.g. 3 and 7).
- Notice that if the first cell turns out to be 3, the second cell is forced to be 7.
- Conversely, if the first cell turns out to be 7, the second is forced to be 3.
- In either outcome, those two digits are completely accounted for by those two cells.
- Erase both candidate digits from all other unsolved cells sharing that same row, column, or box.
Common mistakes
- Applying eliminations across houses that the pair does not mutually share. (For example, if the pair shares a box, eliminations only apply inside that box unless they also share a row or column).
- Assuming the two cells must be adjacent. Naked pairs can be separated across opposite sides of a row or column.
- Overlooking naked pairs because one cell was partially obscured by missing pencil marks.
Frequently asked questions
- Do the two cells of a Naked Pair have to touch?
- No. They only need to be in the same house (same row, same column, or same 3×3 box). They can be on opposite ends of a row.
- What if the two cells share both a row and a box?
- Then you get a double bonus! You can eliminate both candidates from the remaining cells of the row AND from the remaining cells of the box.
- Can a Naked Pair have three candidates?
- No. If cells have three candidates, you are dealing with a Naked Triple or an incomplete pair.
Related techniques
Put Naked Pair into practice
Try a puzzle from the Medium tier (Peak Score 31–40).