A subset in Sudoku is a group of cells confined to an equal number of candidates within a house. This single idea generates pairs, triples, and quads - and explains why each of them eliminates candidates from the rest of the house.
A subset is the umbrella name for the family of pair-, triple-, and quad-based techniques in Sudoku. The pattern is always the same: N cells in a single house share a combined candidate pool of exactly N digits. Those N digits must occupy those N cells, so you can erase them from every other cell in that house.
The N=1 case is a naked single (one cell, one candidate). N=2 is a naked pair, N=3 a naked triple, N=4 a naked quad. Subsets above N=4 exist but never give new information beyond their complement.
A naked subset is found by looking at the cells: N cells whose pencil marks are all subsets of the same N-digit pool. A hidden subset is the same pattern viewed from the other side: N digits that have only N possible cells in a house. Both are the same underlying constraint.
Hidden subsets give you eliminations inside the N cells (drop everything that is not part of the pool), while naked subsets give you eliminations outside them. Most strong solvers learn one and pick up the other later.
Pairs are the most common subset and frequently break a puzzle open. Triples come up in hard puzzles, quads in expert / extreme. Hidden subsets often appear when a puzzle is densely pencil-marked and naked patterns are hard to spot.
For each size, see naked pairs, naked triples, hidden pairs, and hidden triples for worked examples.
Because in any house of 9 cells, an N-cell subset and its (9-N)-cell complement carry the same information. A 5-cell subset is just a 4-cell hidden subset viewed differently. Past N=4, you should look at the complement instead.
Yes - they describe the same constraint from opposite angles. Pick whichever is faster to spot. With sparse pencil marks, naked is easier; with dense pencil marks, hidden is easier.
Pairs are intermediate, triples step into hard territory, quads are advanced. Hidden subsets at any size sit slightly above their naked counterpart because they require flipping perspective.
Look at row 1. Cells C1 and C2 each have only two possible digits: 3 and 7.
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