Naked pairs: Two cells reserving two digits
Use two cells with the same pair of candidates to remove possibilities from their shared unit, with a worked example and exercise.
The condition you need
A naked pair occurs when two cells in the same unit have exactly the same two candidates. For example, each cell contains only {2, 7}. Both cells must be filled, and they cannot repeat a digit, so one will contain 2 and the other will contain 7. You do not yet know their order. You do know that these two digits are reserved for those two cells. You can remove them from every other cell in their shared unit. This technique often produces an elimination before it produces a direct placement.
A worked row example
In row 5, r5c2 and r5c8 each have the complete candidate list {2, 7}. Another cell in that row, r5c4, has {2, 4, 7}. The pair reserves 2 and 7 for r5c2 and r5c8, so both candidates can be removed from r5c4. Only 4 remains, giving r5c4 = 4. You still cannot decide which cell in the pair contains 2. Notice that r5c2 and r5c8 belong to different boxes. This pair supports eliminations in row 5, rather than in both of those boxes.
Why the deduction works
Consider both possibilities without choosing either as an answer. If r5c2 is 2, r5c8 will be 7. If r5c2 is 7, r5c8 will be 2. In both cases, the two digits occupy the two cells of the pair, leaving no place for another 2 or 7 in the row. The elimination holds regardless of the final order. This argument both explains the technique and identifies its limit. Any affected cell must belong to a unit that is shared by both cells of the pair.
Two mistakes to recognise
The lists {2, 7} and {2, 7, 9} do not form a naked pair, because the second cell could still be 9. Finding {2, 7} in two cells that share no row, column or box is also insufficient. If both cells share a row and a box, you can remove 2 and 7 from the other cells in that row and in that box, checking each unit separately. Before using the pattern, confirm that the lists are complete and that any previous eliminations used to produce them have valid explanations.
Try a box exercise
Within one box, r1c1 and r3c2 have only {3, 8}. Cell r2c3 has {3, 5, 8}, while r1c3 has {1, 3, 6, 8}. The pair reduces r2c3 to {5} and r1c3 to {1, 6}. The first cell is solved as 5; the second remains open. Do not remove 3 or 8 from the whole of row 1, because r3c2 does not belong to that row. After placing 5, update its units and search again for singles. A useful elimination can be the move that lets you return to simpler solving techniques.
The first two cells form a naked pair. What remains in r5c8?
r5c1 {2,7} · r5c4 {2,7} · r5c8 {2,5,7}
Now try it on the grid.
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