# Selfish shellfish

**Discrete Mathematics**Level 3

A subset of \(\{1,2,\ldots, 12\}\) is said to be **selfish** if it contains its size as an element. How many subsets of \(\{1,2,\ldots 12\}\) have the property that both the subset and its complement is selfish?

**Details and assumptions**

As an explicit example, the set \(\{3,6,9\}\) is selfish because it contains 3 elements, and contains the element 3.