Here's a fun math problem. I wasn't able to get it - am curious what you guys have to say.
Pick a four-digit number whose digits are not all the same. From its digits form the smallest four-digit number $m$ and the largest, $M$. Find $(M-m)$. Keep repeating the procedure. (Treat, say $234$ as $0234$.) Eventually you will reach $6,174$ - permamently, since:
For example, start with $4,818$:
$7,641-1,467=6,174;$ and so on.
Can you prove that you always reach $6,174$?