Problem

Source: Taiwan 2001

Tags: search, combinatorics unsolved, combinatorics



Let n3 be an integer and let A1,A2,,An be n distinct subsets of S={1,2,,n}. Show that there exists xS such that the n subsets Ai{x},i=1,2,n are also disjoint.

HIDE: what i have is this we may assume that the union of the Ais is S.