MathDB

4

Part of 2000 Greece National Olympiad

Problems(1)

Subsets.

Source: Greece National Olympiad 2000 , Seniors , Problem 4.

11/18/2005
The subsets A1,A2,…,A2000A_1,A_2,\ldots ,A_{2000} of a finite set MM satisfy ∣Ai∣>23∣M∣|A_i|>\frac{2}{3}|M| for each i=1,2,…,2000i=1,2,\ldots ,2000. Prove that there exists m∈Mm\in M which belongs to at least 13341334 of the subsets AiA_i.
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