Techniques / Subsets

Naked Subset (general form)

Also called Disjoint Subset, Naked Set, Subset (naked).

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Find some squares in one row, column or box. Count the numbers left in them. If there are as many squares as numbers, those numbers fill those squares. So they can go nowhere else in that group.

The exact rule, for stronger players

The rule, stated exactly: For a house H and an integer n from 1 to 4, if n cells of H have candidate sets whose union has cardinality exactly n, those n digits may be eliminated from every other cell of H.

What it removes: Remove the n digits from all cells of H outside the subset.

Why it works: The n cells require n distinct digits and only n are available to them, so those digits are entirely consumed by those cells. The naked single is the case n=1.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Naked Subset (general form). r1c2, r1c3 in r1 hold only 2, 7 between them, so those two digits fill those cells and appear nowhere else in r1. — r1c2, r1c3 in r1 hold only 2, 7 between them, so those two digits fill those cells and appear nowhere else in r1.

Sudoku grid showing Naked Subset (general form). r2c2, r2c5 in r2 hold only 3, 7 between them, so those two digits fill those cells and appear nowhere else in r2. — r2c2, r2c5 in r2 hold only 3, 7 between them, so those two digits fill those cells and appear nowhere else in r2.

Learn these first

Naked PairTwo squares in the same group both hold only the same two digits.

Related subsets

Naked TripleThree squares in one group share the same three digits between them.
Hidden PairTwo digits in one group can only go in the same two squares.
Hidden QuadFour digits in a group can only go in the same four squares.
Hidden Subset (general form)Some numbers in a group have only a few homes left.
Hidden TripleThree digits in a group can only go in the same three squares.

How often does it come up?

Our rough estimate: this is the umbrella page, not a separately detected pattern. Frequency is the sum of its instances.

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