A naked pair is two cells in the same row, column, or box that both have exactly the same two candidates left — nothing else. Between the two of them, those two digits have to be placed one each. It doesn’t matter which cell gets which; what matters is that neither digit can appear anywhere else in that unit.

Why it works

Say cells r2c4 and r2c7 are both down to candidates 8, and nothing else. One of them is a 3 and the other is an 8 — there’s no third option for either cell. That means every other cell in row 2 can have 3 and 8 struck off its own candidate list, because both of those digits are already spoken for by this pair, wherever exactly they end up between the two of them.

Worked example

239
4
2589
28
7
69
356
356
1
129
29
6
3
129
5
4
7
8
13
7
58
148
14
46
356
9
2
46
1
3
9
45
8
2
56
7
29
8
29
6
135
7
135
4
39
469
5
7
14
134
2
136
8
369
5
6
1
7
249
349
8
23
34
7
23
24
5
8
1
9
236
346
8
239
249
24
6
34
7
1
5

r5c1 and r5c3 in row 5 can only be 2 or 9, so those digits can be removed from the rest of row 5.

The two cells holding the pair don’t change at all here — the elimination happens to other cells in the same row, column, or box that still listed one of the pair’s digits as a candidate.

How to find one quickly

Look for cells with exactly two candidates — they’re the only ones that can form a naked pair. When you find two in the same unit with the identical pair of digits, check every other cell in that unit for either digit and cross it off. This is also the simplest version of a pattern that scales up: three cells sharing exactly three digits between them is a naked triple, the same idea one size larger.

Hidden pair looks like the reverse of this — two digits confined to the same two cells rather than two cells confined to the same two digits — and the two often show up in the same puzzle without either one ruling the other out. Naked triple is the direct extension once pairs stop finding anything.

Puzzles at Medium are the first level built around needing this.