Question 42
(MON 3) Let $A_k$ $(1\le k\le h)$ be $n$-element sets such that each two of them have a nonempty intersection. Let $A$ be the union of all the sets $A_k$, and let $B$ be a subset of $A$ such that for each $k$ $(1\le k\le h)$ the intersection of $A_k$ and $B$ consists of exactly two different elements $a_k$ and $b_k$. Find all subsets $X$ of the set $A$ with $r$ elements satisfying the condition that for at least one index $k$, both elements $a_k$ and $b_k$ belong to $X$.