USAMO 1983 Problem 3 - Closed intervals
Source: USAMO 1983 Problem 3
August 16, 2011
AMCUSA(J)MOUSAMOcombinatorics unsolvedcombinatorics
Problem Statement
Each set of a finite family of subsets of a line is a union of two closed intervals. Moreover, any three of the sets of the family have a point in common. Prove that there is a point which is common to at least half the sets of the family.