take any four digit number where all the digits are not the same. rearrange them to make the largest # possible. Rearrange them again to make the smallest # possible. Subtract the smaller # from the larger #. Take the result and do it all over again. repeat this process until you hit 6714, you should get stuck there. if you ever get a result less than four digits put a zero in front of it. (999 would be 0999).

Originally posted by palomine take any four digit number where all the digits are not the same. rearrange them to make the largest # possible. Rearrange them again to make the smallest # possible. Subtract the smaller # from the larger #. Take the result and do it all over again. repeat this process until you hit 6714, you should get stuck there. if you ever get a result less than fo ...[text shortened]... - 2237 = 5085

8500 - 5058 = 3442

4432 - 2344 = 2088

8802 - 2088 = 6714

Why is this?

A guess i haven't proved yet; because of these calculations you cycle through all numbers there are. As soon as you have the 1467 you end up in a cycle;

I don't why it is true, but it is easy to prove that all numbers you get are divisible by 9. This is cause the sum of the digits modulo 9 equals the number itslef modulo 9. And the first are the same for both numbers so the difference always equas 0 modulo 9.
Perhaps this might help a bit.