# Small Intersections

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.

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