Mathematical and Physical Journal
for High Schools
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# 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

(5 pont)

Deadline expired on June 16, 2008.

### Statistics:

 2 students sent a solution. 5 points: Lovász László Miklós. 0 point: 1 student.

Problems in Mathematics of KöMaL, May 2008