Naked pair

In a row, column or box, if two cells have exactly the same two candidates, those two digits belong to those two cells. You may not know which goes where yet, but you know for sure that no other cell of the line can take either of them.

Why it works

Say cells A and B in a column both have the candidates {1, 2}. If A is 1, B is 2; if A is 2, B is 1. Either way, 1 and 2 end up in A and B. The column holds each digit once, so the rest of the column can take neither 1 nor 2.

On a real board

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The two blue cells of column 3 hold only 1 and 2. Those two digits must go in these two cells, so they come off every other cell of the line (red). Play this board →

This is a 9×9 · Hard board after filling every naked and hidden single. Candidates are shown for the empty cells of column 3.

Row 5, column 3 and row 8, column 3 both have exactly the candidates 1 and 2. That is a naked pair.
So remove 1 and 2 from the other cells of column 3: 1 from row 1, column 3 and 2 from row 6, column 3.
With those candidates gone, another part of the board opens: row 6, column 9 becomes 2, as a hidden single in row 6.

A naked pair places nothing by itself. But the candidates it removes narrow down other lines, and as here, it often unlocks a cell some distance away.

The cells don't need to be neighbours

The two cells only need to share a row, a column or a box. If they share a box and a row, you can remove the two digits from both the row and the box.

Triples and quads

The same idea works with three cells. If three cells in a line have only three different digits between them, for example {3, 7}, {3, 8} and {7, 8}, those three digits belong to those three cells and can be removed from the rest of the line. This is a naked triple. The tricky part is that each cell does not need all three digits; three digits in total is enough.

Spotting it

Look for cells with exactly two candidates first. When you find one, check its row, column and box for a twin.
Lines with many empty cells pay off most, because there is more to remove.
Remember pairs you have found. The same pair can work in another direction, a box instead of a row.

Common mistake: treating {1, 2} and {1, 2, 5} as a pair. Both cells must have exactly the same two digits. Grouping a third cell into three digits is a triple, which is a different check.

Where you need it

Alongside locked candidates on 9×9, 12×12 and 16×16 Hard boards. Looked at the other way round, a naked pair becomes the hidden pair, next.