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.
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.