Question 94
Let $A_{1}, A_{2}, \ldots, A_{n}$ be finite sets such that
$$
\left|A_{i} \cap A_{i+1}\right|\gt \frac{n-2}{n-1}\left|A_{i+1}\right|
$$
for any $i=1,2, \ldots, n$ ($A_{n+1} \equiv A_{1}$). Prove that their intersection is a nonempty set.
$$
\left|A_{i} \cap A_{i+1}\right|\gt \frac{n-2}{n-1}\left|A_{i+1}\right|
$$
for any $i=1,2, \ldots, n$ ($A_{n+1} \equiv A_{1}$). Prove that their intersection is a nonempty set.