A. 531. Prove that for every positive integer k there is a positive integer Nk (depending only on k) such that whenever is a set system whose elements are at most k-element sets such that every two elements of have an element in common, then there exists a set A with at most Nk elements such that every two elements of and A have an element in common.
(Proposed by: Ambrus Zsbán, Budapest)
Deadline expired on 11 April 2011.