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 \mathcal S and \mathcal T consist of p subsets of H such that these 2p subsets are pairwise distinct. Suppose that for every A\in \mathcal S and B\in \mathcal T, the sets A and B have at least one common element. Show that \frac{p}{2^n}<\frac{3-\sqrt{5}}{2}.

Proposed by Ilya Bogdanov, Moscow

(5 pont)

Deadline expired on June 16, 2008.


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

Problems in Mathematics of KöMaL, May 2008