If two cells in a box, row or column hold nothing but the same two candidates, those two digits belong to those two cells, so every other cell in that house loses both of them.
How to spot it
You find a naked pair by reading cells, not by counting digits. A cell that is down to two candidates is half a pair already, and the other half is a second cell in the same house showing the same two digits.
That is the reverse of the question a hidden single asks. There you take a digit and ask where it can still go, which means checking every empty cell in the house, once for each digit still missing. Here you take a cell and ask what it has left, and the answer is already written inside the cell. Two-candidate cells are rare enough to stand out and cheap enough to check. On the row below there are two of them among five empty cells, and the digit-counting scan finds nothing there at all.
Read the house cell by cell
Row one has five empty cells and five digits still missing, so counting digits means twenty-five cells to check and it ends with nothing: not one of those five digits is down to a single home. Reading cells, you stop at the first one that is down to two candidates.
Look for the same two digits again
The next cell along shows 3 and 5 as well, and nothing else. Two cells, the same two candidates, one house.
Two digits, two cells
One of these cells takes the 3 and the other takes the 5. You do not need to know which way round. Row one holds one 3 and one 5 in total, and both are now accounted for.
Cross both digits out of the rest of the house
Four marks go: a 5 from the sixth cell, a 3 and a 5 from the seventh, a 3 from the ninth. Nothing changes in the two cells that started this.
Read the row back
The seventh cell was showing 3, 5 and 9. It is now showing 9 on its own, which places a digit. The pair itself still reads 3 and 5, exactly as it did before.
Nothing is ever removed from the pair's own two cells. If you find yourself rubbing something out inside them, the pattern you have is a hidden pair, which is the same fact read from the other end and does the opposite job.
The answer is not where you found it
The cells that make a naked pair are not the cells it changes.
A hidden single finishes in the cell you were staring at: you found it, you wrote the digit in. A naked pair finishes somewhere else entirely. The two cells that carry the evidence read 3 and 5 before the technique and 3 and 5 after it, and the boards above say so. Every edit lands in cells that never entered the search.
That is worth saying out loud, because it is what makes this technique easy to find and easy to stop halfway through. Finding the pattern does not finish anything. It only tells you that two candidates can now come out, four cells away. Look back at the pair, see that nothing about it has changed, and it is very easy to decide the work is done. On this board the payoff is the 9 in the seventh cell, and it is only there if you crossed the digits out.
Two cells, two houses
There is a second reason to be careful about where you act, and this board shows it.
The two cells that made this pair sit in row one. They also sit in box one. Both of those are houses, and the argument does not prefer one over the other: a 3 and a 5 are accounted for in the row, and the same 3 and 5 are accounted for in the box. So you cross both digits out twice, over two different sets of cells.
Row one gives up four candidates. Box one gives up three more, in two cells that are not in row one at all. The second pass is the one that does the most here: it leaves both of those cells holding 1 and 6, which is a fresh naked pair in column one, made by the first one. A reader who cleans the row and moves on has done a little over half the work, and there is no sign of it on the board.
Whenever the two cells of a pair share a box as well as a line, check both.
Four candidates in three cells, spread the width of the grid.
Three more, in two cells the row never touched. Same pair, same argument.
A different box. The two marked cells hold nothing but a 1 and a 9. What comes off the board?
Ask which cells the two digits are now unavailable to.
Recap
- Look for
- Two cells in the same house showing the same two candidates and nothing else.
- Scope
- Any house: box, row or column. Check every house the two cells share, which is often two.
- Result
- Both digits come out of every other cell in that house. The pair itself is left untouched.
- Tell-tale
- A house with two cells down to two marks each. You read it off the pencil marks without counting anything.
- If it fails
- If the two cells show the same two digits but a third cell in the house shows them too, that third cell has to be considered as well and you may be looking at a naked triple. If nothing else in the house carries either digit, the pair is real but removes nothing there, and the house to check is the other one the two cells share.