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.

An alternate line of attack is to prove that for any number ending in 1,3,7,9 there is a multiple of the form 10^n + 1.  (Or a*10^n + b for some digits a,b).

Posted by Jer on 2019-09-10 11:20:41