A number $ B$ is obtained from a positive integer number $ A$ by permuting its decimal digits. The number $ A-B=11...1$ ($ n$ of $ 1's$). Find the smallest possible positive value of $ n$.
Source: Russian 2007
Tags: number theory proposed, number theory
A number $ B$ is obtained from a positive integer number $ A$ by permuting its decimal digits. The number $ A-B=11...1$ ($ n$ of $ 1's$). Find the smallest possible positive value of $ n$.