Naked Pair
When two cells in the same unit share exactly the same two candidates, those two digits can be eliminated from other cells in that unit.
A Naked Pair occurs when two cells in the same row, column, or block contain exactly the same two candidate digits and no others. Since these two digits must occupy those two cells, they can be eliminated as candidates from all other cells in the same unit.
Principle and Application
For example, if two cells in a row both have only candidates {3, 7}, then 3 and 7 must go in one of these two cells. Therefore, no other cell in that row can contain 3 or 7. This elimination often creates Naked Singles in other cells.
Tips for Spotting Them
Identify all cells with exactly two candidates, then check whether any pair in the same unit shares the same candidates. Accurate pencil marks are a prerequisite. This technique is essential for solving Hard-level puzzles.
A Worked Example on the Board
- The two cells whose only candidates are {1, 6}
- Cells that lose 1 and 6 as candidates
Empty cells are still open. r7c5 narrows to {3, 7} and r8c2 is fixed at 8.
Look at the second and third cells of row 7 in the board above (r7c2 and r7c3).
Count the candidates for r7c2: row 7 already holds 9, 2 and 8; column 2 holds 3, 7, 5, 2 and 4; and the bottom-left block holds 9, 2, 7, 3, 4 and 5. Only {1, 6} survives, and the same count leaves r7c3 with {1, 6} as well. That is a naked pair. Since 1 and 6 must occupy these two cells, no other cell in row 7 can take them, so the candidates of r7c5 shrink from {1, 3, 6, 7} to {3, 7}.
The two cells also share a block, so the elimination works inside the block too. Just below them, r8c2 held {1, 8}; with the 1 gone it is fixed at 8 (a naked single). A naked pair never tells you which of the two cells takes which digit, and it does not need to: its value lies in the chain of eliminations it sets off around it.
How It Differs from a Hidden Pair
| Aspect | Naked pair | Hidden pair |
|---|---|---|
| Definition | Two cells are left with the same two candidates only | Two digits fit in only the same two cells of a unit |
| How the marks look | Just two candidates, out in the open | Mixed in with other candidates, out of sight |
| Where candidates go | The two digits leave the other cells of the unit | The other candidates leave the two cells of the pair |
| Where to start looking | From a cell (cells with only two candidates) | From a digit (digits with only two possible cells) |
The real difference is the direction of the elimination: clearing the surplus candidates of a hidden pair turns it into a naked pair.
A naked pair is defined from the cells: two cells hold nothing but the same two candidates. A hidden pair is defined from the digits: within one unit, two digits can only go into the same two cells. In a hidden pair those two cells usually carry other candidates as well, which is exactly why the pair stays hidden among the pencil marks.
The elimination then runs the other way. A naked pair clears those two digits from the rest of the unit; a hidden pair clears every other candidate from the two cells themselves. Once the surplus candidates are gone, a hidden pair simply becomes a naked pair, so the two patterns are two views of the same situation.