Singles carry an easy puzzle almost to the end, but on a Hard board (28 to 32 givens) you will eventually reach a position where every blank cell has two or more candidates and none of them is forced. A naked pair is usually the way through. It happens when two cells in the same row, column or box both have exactly the same two candidates, say 4 and 6, and nothing else.
Those two digits have to fill those two cells, in one order or the other. It does not matter which cell gets which digit; what matters is that neither 4 nor 6 can be anywhere else in that row, column or box. Any other cell in the unit that still lists 4 or 6 as a candidate can have it crossed off, even if that cell is nowhere near solved.
Naked pairs do not usually place a digit by themselves. What they do is strip candidates away from other cells, which often exposes a hidden or naked single a step or two later. On the Hard Sudoku board, this is frequently the move that gets a stalled puzzle moving again.
Worked example
A real Hard puzzle (30 givens). Row 5 has a naked pair; step through finding it and see what it clears from the rest of the row.
Spotting a naked pair
Naked pairs hide in plain sight once you know to look for them. Scan a row, column or box and compare the candidate lists of its blank cells. You are hunting for two cells, and only two, that share an identical two-digit list. Three candidates do not count, and a list of two that only partly matches another cell's list does not count either. The match has to be exact.
Boxes tend to be the easiest place to spot them, since you are comparing at most nine cells at once, but the same pattern turns up across full rows and columns too, especially once pencil marks are filled in for the whole board.
Why the elimination is always safe
The logic behind a naked pair does not depend on guessing which cell gets which digit. Suppose cells A and B are the only two cells in a unit still listing 4 and 6. If some other cell C in that unit were also 4, then A and B would have to split 6 between them, which is impossible since they cannot both hold the same digit. The same argument rules out 6 in any other cell. So both digits are locked to A and B no matter how the puzzle eventually resolves, and every other cell in the unit is safe to clear of them.
Common mistakes
- Matching cells with three or more candidates. A naked pair needs exactly two candidates in each cell. Two cells that both include 4 and 6 among three or four options are not a pair yet, and clearing 4 or 6 elsewhere based on them is not valid.
- Clearing candidates outside the unit. A pair found inside a box only clears digits from that box. If the two cells also happen to sit in the same row, the row is a second unit and can be cleared too, but a cell that merely shares a row with one of the pair cells is not affected.
- Stopping at the pair instead of using it. Finding a naked pair is not the end of the move. Go back through every other cell in that row, column or box and cross off both digits wherever they still appear; that is the actual payoff.
What comes after a naked pair
Removing a digit from three or four cells rarely finishes a puzzle outright, but it often exposes a naked or hidden single nearby, or sets up a further naked pair or pointing pair elsewhere on the board. Re-scan the row, column and box you just touched before moving on, since the elimination you made can ripple into a placement one or two moves later.
If naked pairs are not turning up on a puzzle that feels stuck, it usually means the pencil marks are incomplete somewhere. Go back over the crowded cells and check all nine digits again.
Hard boards (28 to 32 givens) are exactly where singles run dry and naked pairs start doing the real work. Fill in Notes and watch for matching two-digit lists.
Frequently asked questions
A naked pair is two cells in the same row, column or box that both have exactly the same two candidates and nothing else. Those two digits must fill those two cells, so neither can appear anywhere else in that unit.
Usually not. It removes both paired digits as candidates from the rest of the unit, which often reveals a naked or hidden single a step or two later rather than solving a cell immediately.
A naked pair is two cells whose entire candidate list matches, just two digits each. A hidden pair is two digits confined to the same two cells within a unit, even though those cells may still list several other candidates too.
No. They only need to share a unit, meaning the same row, the same column, or the same box. They can sit anywhere within that unit.
Hard boards start with fewer givens (28 to 32), so cells hold onto multiple candidates for longer and singles run out sooner. Naked pairs are usually the first technique beyond singles that a Hard puzzle requires.
No, that pattern is called a naked triple and works a little differently: three cells sharing candidates drawn from the same three digits, not necessarily with all three digits in every cell.