Locked Subsets

Locked subsets: N cells sharing N candidates (naked) or N digits sharing N positions (hidden) inside one house — pairs, triples and quadruples.

A naked pair of candidates 1 and 2 eliminates those candidates from other cells in a Sudoku column

Naked Pairs

Two matching two-candidate cells that eliminate peers.

Hidden Pair

Two digits restricted to two cells in one house.

Naked Triple

Three cells containing only three combined candidates.

Hidden Triple

Three digits confined to three cells in one house.

Four Sudoku cells whose combined candidates contain only four digits

Naked Quad

Four cells restricted to four combined candidates.

Four digits confined to four cells inside one Sudoku house

Hidden Quad

Four digits confined to four cells in one house.

One theorem, all sizes

A locked subset balances N objects with N possibilities inside one house. In the cell view, N cells have a union of N candidate digits: a naked subset removes those digits from the other cells of the house. In the positional view, N digits have a union of N positions: a hidden subset removes all other candidates from those cells.

Pairs, triples and quadruples are the same theorem at N = 2, 3 and 4 — a Quad is not a more advanced rule, just a larger instance that is rarer and harder to spot. The related fish constructions (X-Wing, Swordfish, Jellyfish) apply the same accounting across several houses and have their own group.

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