Naked pairs and triples

Two cells holding the same two candidates own both digits between them. Everything else in the unit loses them.

The idea

Suppose two cells in the same row both have exactly the candidates 3 and 7. You do not know which is which — but between them they will take both digits. So no other cell in that row can be a 3 or a 7, and you can strike those candidates out.

Two cells in this unit share the same pair of candidates, so those digits are removed from the marked cells.

Triples work the same way

Three cells whose candidates between them use only three digits lock those three digits into those three cells. The cells do not each need all three: {2,5}, {5,9} and {2,9} is a valid triple, and so is {2,5,9}, {2,5} and {5,9}. What matters is that the union is exactly three digits across exactly three cells.

Where to look

  • Units where you have already written candidates — pairs are almost invisible without them.
  • Cells with exactly two candidates. Scan a unit for those first, then compare them to each other.
  • Boxes as well as rows and columns; a pair in a box is as useful as one in a line.

The most common mistake

A naked pair must be exactly two candidates in each of the two cells. If one cell has {3,7} and the other {3,7,8}, it is not a naked pair — the second cell might be an 8, and the argument collapses. That case may still be a hidden pair, which is a different move with a different test.

These are the moves that decide a hard puzzle.

Common questions

What is a naked pair?

Two cells in the same row, column or box that each have exactly the same two candidates. Those two digits can be removed from every other cell in that unit.

What is a naked triple?

Three cells in one unit whose candidates together use exactly three digits. Those digits can be removed from the rest of the unit.

Do all three cells need all three candidates?

No. Each cell needs at least two of them, and the union across the three cells must be exactly three digits.

What if one cell has an extra candidate?

Then it is not a naked pair. Check for a hidden pair instead, which allows extra candidates and eliminates them.