IMO 1976 LL NET24

Let 0 \leqx1 \leqx2 \leq\cdot \cdot \cdot \leqxn \leq1. Prove that for all A \geq1

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IMO 1976 LL NET24

Origin: NET

Problem

Let 0 \leqx1 \leqx2 \leq\cdot \cdot \cdot \leqxn \leq1. Prove that for all A \geq1 there exists an interval I of length 2 n\sqrt A such that for all x \inI, |(x −x1)(x −x2) \cdot \cdot \cdot (x −xn)| \leqA.