Naked Pairs in Sudoku
Naked pairs are a powerful elimination technique used in medium and hard sudoku. Once you understand them, you'll unlock deductions that would otherwise seem impossible using single-cell analysis alone.
What Is a Naked Pair?
A naked pair occurs when two cells in the same row, column, or box both contain exactly the same two candidates — and only those two.
For example: if cell A contains candidates {3, 7} and cell B in the same row also contains exactly {3, 7} — those two cells form a naked pair. One of them must be 3 and the other must be 7. We don't know which is which yet, but we know for certain that no other cell in that row can be 3 or 7.
This lets you eliminate 3 and 7 from the candidates of every other cell in the shared row, column, or box.
Why Does This Work?
Because the two cells must together account for both digits, those digits cannot appear anywhere else in the group. If a third cell in the same row were also a 3, then when the naked pair resolves, one row would contain two 3s — a rule violation. Therefore, 3 and 7 can safely be eliminated from all other cells in that group.
How to Find Naked Pairs
- Fill in pencil marks (candidates) for all empty cells.
- Look for cells that contain exactly two candidates.
- Check if any other cell in the same row, column, or box contains exactly the same two candidates.
- If found — you have a naked pair. Eliminate both digits from all other cells in that shared group.
Naked pairs require pencil marks to find reliably. Trying to spot them mentally on harder puzzles is error-prone.
Example
In a row, five cells are already filled (1, 7, 6, 4, 9), leaving four empty cells. After applying row, column, and box eliminations, the candidates are:
- C2: {2, 8} — column 2 already contains a 3 (above) and a 5 (below), eliminating both
- C4: {2, 5, 8} — column 4 already contains a 3 (above), eliminating 3
- C6: {2, 3, 8} — column 6 already contains a 5 (below), eliminating 5
- C8: {2, 8} — column 8 already contains a 3 (above) and a 5 (below), eliminating both
C2 and C8 both contain exactly {2, 8} — a naked pair (amber below). One of them is 2 and the other is 8; both digits are now claimed by this pair and cannot appear anywhere else in the row. Eliminating 2 and 8 from the other empty cells:
- C4: {2, 5, 8} → remove 2 and 8 → {5} — a naked single!
- C6: {2, 3, 8} → remove 2 and 8 → {3} — a naked single!
One naked pair — two naked singles resolved at once. This is the power of naked pairs.
Naked Pairs in Boxes
Naked pairs work identically in 3×3 boxes. If two cells in the same box contain exactly the same two candidates, those candidates can be eliminated from all other cells in that box. This is often easier to spot visually because the nine cells are clustered together.
Naked Triples
The same logic extends to three cells. A naked triple occurs when three cells in a group collectively contain only three distinct candidates. The cells don't each need to have all three — any combination works as long as the union of candidates across all three cells contains exactly three digits.
For example: {1,2}, {2,3}, {1,3} is a naked triple using digits 1, 2, and 3. Eliminate 1, 2, and 3 from all other cells in the group.
When to Use Naked Pairs
Naked pairs appear on medium and hard puzzles, typically after naked singles and hidden singles are exhausted. If you're stuck and pencil marks are in place, scanning for two-candidate cells and checking for pairs is a reliable next step.