IMO 1989 LL FRA19

Let a1, . . . , an be distinct positive integers that do not contain

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IMO 1989 LL FRA19

Origin: FRA

Problem

Let a1, . . . , an be distinct positive integers that do not contain a 9 in their decimal representations. Prove that a1

  • \cdot \cdot \cdot + 1 an \leq30.