Question 25
(NZL) Let $U=\{1,2,\ldots,n\}$, where $n\ge3$. A subset $S$ of $U$ is said to be split by an arrangement of the elements of $U$ if an element not in $S$ occurs in the arrangement somewhere between two elements of $S$. For example, $13542$ splits $\{1,2,3\}$ but not $\{3,4,5\}$. Prove that for any $n-2$ subsets of $U$, each containing at least $2$ and at most $n-1$ elements, there is an arrangement of the elements of $U$ that splits all of them.