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?

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