Let $A_1, A_2, ..., A_k$ be $5$-element subsets of set $\{1, 2, ..., 23\}$ such that, for all $1 \le i < j \le k$ set $A_i \cap A_j$ has at most three elements. Show that $k \le 2018$.
Problem
Source: 69 Polish MO 2018 Second Round - Problem 5
Tags: combinatorics, set theory, pigeonhole principle, Poland, counting