A shrinkable number is one that can be reduced to a single digit by the following process:

Create a new number where each digit is the absolute difference between consecutive digits.
Repeat until you have a single digit.
No digit is allowed to be a zero at any point in the process.

Examples:
7624 is shrinkable. It reduces to 142 which reduces to 32 which reduces to 1.
4131 is not shrinkable because it reduces to 322 which reduces to 10 which contains a zero.

Your goal is to create the smallest possible n digit shrinkable number for n = 2, 3, 4, ...
Is there a shrinkable number for any value of n?

(In reply to answer by Dej Mar)

n=9

1 3 9 2 1 9 2 1 6
 2 6 7 1 8 7 1 5
  4 1 6 7 1 6 4
   3 5 1 6 5 2
    2 4 5 1 3
     2 1 4 2
      1 3 2
       2 1
        1

Posted by Charlie on 2011-04-05 18:13:00