# Small Intersections

**Discrete Mathematics**Level 5

Let \( S = \{ 1, 2, 3, \ldots 11 \} \) and \( T_1, T_2 \ldots, T_N \) be distinct subsets of \(S\) such that \( | T_i \cap T_j | \leq 2\) for all values \( i\neq j \). What is the maximum possible value of \(N\)?

**Details and assumptions**

If you are unfamiliar with the set notation symbol \( \cap \), you may refer to Venn Diagram for an explanation of the intersection symbol.

The empty set is a subset of every set.