MathDB

Subsets.

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

November 18, 2005

combinatorics proposedcombinatorics

Problem Statement

The subsets

A_1,A_2,\ldots ,A_{2000}

of a finite set

M

satisfy

|A_i|>\frac{2}{3}|M|

for each

i=1,2,\ldots ,2000

. Prove that there exists

m\in M

which belongs to at least

1334

of the subsets

A_i