Problem A. 531. (March 2011)

A. 531. Prove that for every positive integer k there is a positive integer N_k (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 N_k elements such that every two elements of  and A have an element in common.

(Proposed by: Ambrus Zsbán, Budapest)

(5 pont)

Deadline expired on April 11, 2011.

Statistics:

7 students sent a solution.
5 points:	Ágoston Tamás, Backhausz Tibor, Frankl Nóra, Janzer Olivér, Mester Márton, Nagy 235 János.
4 points:	Nagy 648 Donát.

Problems in Mathematics of KöMaL, March 2011