olymmath

RU-ALLRUSSIAN 1983 Problem 20

    X is a union of k disjoint intervals of the real line. It has the property that for any h<1\mathrm{h}< 1 we can find two points of X which are a distance h apart. Show that the sum of the lengths of the intervals in X is at least 1/k1 / \mathrm{k}

    Dataset text NuminaMath olympiads. Quoted with source.

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