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One may perform the following two operations on a natural number:

For any natural number n, can one perform a sequence of these operations that will transform n to a one-digit number?

- Multiply it by any natural number;
- Delete zeros in its decimal representation.

Source:1991 Leningrad Mathematical Olympiads

This seems to be a hard one. One week after the original posting (May 2, 1997), Tom Halverson had received no solutions (either via email or by Macalester students). Here is a way to turn 11 into a single digit number.

- multiply by 82 to get 902.
- delete the 0
- multiply by 9 to get 828
- multiply by 25 to get 20700
- delete the 0s to get 27
- multiply by by 4 to get 108
- delete the 0 to get 18
- multiply by 5 to get 90
- delete the 0
© Copyright 1997 Stan Wagon. Reproduced with permission.

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2 October 1998