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Putnam 1980 B4

Source: Putnam 1980

April 1, 2022

Putnamset theory

Problem Statement

Let

A_1 , A_2 ,\ldots, A_{1066}

be subsets of a finite set

X

such that

|A_i | > \frac{1}{2} |X|

for

1\leq i \leq 1066.

Prove that there exist ten elements

x_1 ,x_2 ,\ldots , x_{10}

of

X

such that every

A_i

contains at least one of

x_1 , x_2 ,\ldots, x_{10}.

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