Competition problem — Number theory

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Number theory Difficulty 5.4 AIME, harder Prove it

Shapovalov A.V.

A natural number was increased by $10 \%$ and the result was again a natural number. Could the sum of the digits have decreased by exactly $10 \%$ in this process?

Solution

Examples: $998888888880, 99999906666660, 8 \ldots .80$ (45 eights).

## Answer

It could.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.