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?