Problem A. 455. (May 2008)
A. 455. Let H be a set with n elements and let each of the families and consist of p subsets of H such that these 2p subsets are pairwise distinct. Suppose that for every and , the sets A and B have at least one common element. Show that .
Proposed by Ilya Bogdanov, Moscow
Deadline expired on 16 June 2008.