Pair hidden pair

Two pairs of one symbol confined to two cells lock those cells

How to use it

The orthogonality twin of the hidden pair, read on one symbol's pairs. Take a letter, say A: its not-yet-placed pairs each have candidate homes (the cells that could host the pair). If two of A's pairs — say A3 and A5 — have all their homes inside the same two cells, those two cells take exactly those two pairs; every other pair of that symbol is blocked there; other candidates at those cells die as the fallout lands.

Do the same for a digit's unplaced pairs. The pattern appears once a symbol is half-placed: with A already pinned in most rows, its leftover pairs share the few remaining cells, and a two-cell confinement locks them.

Why it is sound

For one symbol, its unplaced pairs must each be placed at one of their homes. If two pairs have all their homes inside the same two cells, those cells carry exactly those two pairs in every solution; every other pair is impossible there and can be blocked. Sound by orthogonality: each cell carries one pair and each unplaced pair must be placed exactly once, so two pairs with homes inside two cells fill them.

A worked example

Take the letter D and its unplaced pairs. D2 and D3 survive only at r4c2 and r5c3 between them — two pairs of one symbol confined to two cells lock those cells, and the cells are spoken for. The blocks fall immediately: D5 is ruled out at r4c2, D1 at r5c3, and at those two cells any candidate that cannot participate in one of the two pairs dies — digit 5 falls at r4c2, digit 1 at r5c3, both by pair elimination with the newly blocked pairs cited as the reason.