HMMT 2003 T6

Prove that any 2 -configuration containing $e$ elements is $m$ -separable for some $m \leq$ $\frac{1}{2}+\sqrt{2 e+\frac{1}{4}}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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m \leq \frac{1}{2} + \sqrt{2e + \frac{1}{4}}

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