IMO Shortlist 1998 problem C4

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2. travnja 2012.
Let U=\{1,2,\ldots ,n\}, where n\geq 3. 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 which splits all of them.
Izvor: Međunarodna matematička olimpijada, shortlist 1998