Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 396. (March 2006)

A. 396. The elements of families \mathcal{A} and \mathcal{B} are finite sets, each having at most n elements. Suppose that for an arbitrary finite set F there exist X\in\mathcal{A} and Y\in\mathcal{B} such that X\capY\capF=Ø. Prove that there exist X\in\mathcal{A} and Y\in\mathcal{B} such that X\capY=Ø.

(5 pont)

Deadline expired on April 18, 2006.


Statistics:

6 students sent a solution.
5 points:Erdélyi Márton, Gyenizse Gergő, Nagy 224 Csaba, Paulin Roland.
3 points:1 student.
2 points:1 student.

Problems in Mathematics of KöMaL, March 2006