Naked pairs
The first genuinely intermediate technique, and the one most hard puzzles are gated behind. Two squares that share the same two candidates between them consume both digits — which tells you something about every other square in the unit.
The idea
Suppose two squares in the same row both show exactly 3 and 8, and nothing else. You cannot tell which is which. But you do not need to: between them they will use up that row's 3 and its 8, in one order or the other.
So no other square in that row can be a 3 or an 8. You have placed nothing, and yet the row is meaningfully more constrained than it was.
A worked example
The pair at r4c1 and r4c2 clears 3 and 8 out of the rest of the row. Look at what that does to r4c7: it was {1,3}, and losing the 3 leaves a naked single. The 1 can be placed immediately.
This is the usual rhythm of the technique. Naked pairs rarely place a digit themselves; they collapse some other square into a placement.
Triples and quads
The same logic extends. Three squares whose candidates are drawn from a set of three digits form a naked triple; four squares over four digits form a quad.
The subtlety that catches people out: the squares do not each need the full set. Three squares showing {3,8}, {3,9} and {8,9} are a perfectly good triple over {3,8,9} — three squares, three digits between them, so those three digits belong to those three squares. Only the union has to have the right size.
How to spot them
Look for squares with exactly two candidates first; they are the raw material, and a unit containing two of them is worth a second's check. Pairs are much easier to find than triples, and finding pairs is usually enough — a hard puzzle rarely requires a quad.
Common mistakes
The classic error is treating two squares that merely share a candidate as a pair. {3,8} and {3,5} are not a naked pair: between them they use 3 and one of 8 or 5, which constrains nothing. Both squares must be limited to the same two digits.
The other is applying the elimination to the wrong unit. A pair only clears the unit both squares share. If they happen to share a row and a box, you get both — but check that they really do before erasing.
Common questions
What is a naked pair in Sudoku?
Two squares in the same unit whose candidates are the same two digits. Between them those two squares must use both digits, so neither digit can appear anywhere else in that unit and both can be erased from every other square in it.
What is a naked triple in Sudoku?
The same argument run with three squares and three digits. If three squares in one unit use only three candidates between them, those three digits are committed to those three squares, and they can be erased from the rest of the unit.
Does every square in a naked triple need all three digits?
No, and assuming otherwise is the usual reason triples get missed. The squares may show any subsets, so 1-2, 2-3 and 1-3 is a perfectly good naked triple. What matters is that the three candidate lists together contain exactly three different digits.
Where does the elimination apply?
Only inside the unit the squares share. If the two squares of a pair happen to share both a row and a box, then they share two units, and the digits can be erased from the rest of both.
Where to go next
The next technique in the order is hidden pairs — Two digits that can only go in the same two squares — so everything else in those squares goes.
Coming to this cold? The step before it is notes, and this technique is usually the one you reach for when that stops opening squares.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board. Run a puzzle site? Embed this board.
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