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Casting Out Zeros (Posted on 2013-07-25) Difficulty: 4 of 5
One may perform the following two operations on a natural number:

1.Multiply it by any natural number
2.Delete zeros in its decimal representation.

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

No Solution Yet Submitted by Danish Ahmed Khan    
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Godel strikes again | Comment 1 of 4
After playing with this for a while, I suspect that it is true.  I also suspect that it cannot be proven.  I am trying to prove that every 2 digit number can be turned into a one digit number, but 31 and 33 are not yet cooperating.
  Posted by Steve Herman on 2013-07-25 21:43:36
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