IMO 1979 LL CZS14

Origin: CZS

Problem

Let S be a set of n2 + 1 closed intervals (n a positive integer). Prove that at least one of the following assertions holds: (i) There exists a subset S′ of n + 1 intervals from S such that the inter- section of the intervals in S′ is nonempty. (ii) There exists a subset S′′ of n + 1 intervals from S such that any two of the intervals in S′′ are disjoint.