Suppose that we have two operations that we can perform on an integer:

- Multiply it by any positive integer.
- Delete the 0's in its decimal representation.

Beginning with any positive integer can we always obtain a single-digit number after a finite number of operations? For example, beginning with 7, we can multiply by 15 to obtain 105, delete the 0 to get 15, multiply by 2 to get 30, then delete the 0 to end with 3.

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Source: Leningrad Mathematical Olympiad
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