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Complex problems can often be solved by finding ways to split them into several smaller problems. In a Sudoku, each house is a problem that has 362880 possible solutions (the possible permutations for the 9 digits). To reduce this number, a player will try to isolate groups of cells and digits from the remainder of the house.

When N cells and N digits are isolated, a subset of size N is formed.

Alternative terms are disjoint subset, locked set and number chain.

Subset Techniques

There are 2 solving techniques that are focused on subsets:

Naked Subset
N cells with candidates for only N digits.
Hidden Subset
N digits that only have candidates in N cells.

Naked and hidden subsets are complementary. When a house with 7 unsolved cells has a naked subset of size 3, it also contains a complementary hidden subset of size 4.

Fish and Subsets

Fish and Subsets are complementary to each other. One can transform a problem of finding a fish into a problem of finding a subset, and vice versa. See Fish and Subsets for more.

See Also