Kaprekar's Constant

I've been watching the University of Nottingham videos by Brady Haran on physics and chemistry for a while now but I hadn't come across this channel, numberphile before which is, rather unsurprisingly, about numbers.

So for the first thing I've learnt today, it's Kaprekar's constant. Take any four digit number, excluding numbers where all the digits are the same (0000, 1111, 2222, etc). Make the largest number and the smallest number out of these digits. Subtract them and repeat the process until it converges, that is you get the same number again. That number will always be 6174.

For example, take 2395. Rearrange the digits to make 9532 and 2359.
9532-2359 = 7173, and repeat
7731-1377 = 6354
6543-3456 = 3087
8730-0378 = 8352
8532-2358 = 6174
7641-1467 = 6174, and as we had this on the line above, we'll always get 6174 so the process has converged.

For more details, and an expansion to numbers with a different number of digits, see http://plus.maths.org/content/mysterious-number-6174.