# Subset

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.