olymmath

RU-ALLRUSSIAN 1983 Problem 21

    x is a real. The decimal representation of x includes all the digits at least once. Let f(n) be the number of distinct n- digit segments in the representation. Show that if for some n we have f(n)≤n+8\mathrm{f(n)}\leq \mathrm{n} + 8 , then x is rational.

    Dataset text NuminaMath olympiads. Quoted with source.

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