## IMC 2014 Day 2 Problem 1

For a positive integer denote its -th decimal digit by , i.e. and . Suppose that for some sequence there are only finitely many zeros in the sequence . Prove that there are infinitely many positive integers that do not occur in the sequence .

**IMC 2014 Day 2 Problem 1**

Hint: Since it follows that (for large enough).

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