Take any four digit number (whose digits are not all identical), and do the following:
- Rearrange the string of digits to form the largest and smallest 4-digit numbers possible.
- Take these two numbers and subtract the smaller number from the larger.
- Use the number you obtain and repeat the above process. What happens if you repeat the above process over and over?
Amazing thing is this: every four digit number whose digits are not all the same will eventually hit 6174, in at most 7 steps, and then stay there!