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Grid technique · Advanced

Locked Set

The same idea as a locked pair, extended to three or more items: if k items between them can only reach k possibilities, those k possibilities belong to them.

Why it works

Counting the union, not the individual rows, is what makes this work. Three items don't each need three options — between them, touching exactly three possibilities is enough.

Trigger

Several rows or columns in one mini-grid have each shrunk to two or three live candidates.

Common mistake

Counting the union of candidates incorrectly — missing one column makes a real locked set invisible, and adding one turns nothing into a false pattern.

Example

Mina: llama or cat. Theo: cat or turtle. Rae: llama or turtle. Between them, three people touch exactly three pets, so everyone else is excluded from all three, even though no one person has three options.

Put it to work

See this technique on a live board, or go back and browse the rest of the library.