Turkey NMO 2017 p1
Source:
January 26, 2018
combinatorics
Problem Statement
A wedding is going to be held in a city with types of meals, to which some of the citizens will be invited. All of the citizens like some meals and each meal is liked by at least one person. A " " is a set of citizens, such that each meal is liked by at least one person in the set. A " " is a set that contains at least one person from each " ". Given a " ", which has no subset (other than itself) that is also a " ", prove that there exists a meal, which is liked by everyone in the group.