Take a 4-digit number whose digits are not all the same; in other words, a 4-digit number besides 1111, 2222, … 9999. Rearrange the digits first in ascending order and then in descending order to get two numbers. Subtract the smaller from the larger and then repeat the process.
For example, take 4050 and rearrange them as above to get 0045 and 5400 respectively. Now,5400 - 0045 = 5355
5553 - 3555 = 1998 (rearranging the result above, 5355)
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174 (starts recurring)
For 1011,1110 - 0111 = 0999
9990 - 0999 = 8991
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174 (starts recurring)
In other words, the result is that you always end up with the very mysterious 6174. The mathematician who discovered this curious property in 1949 was Dattathreya Ramchandra Kaprekar or D. R. Kaprekar, a school teacher from Maharashtra with a passion for number theory. 6174 is therefore also known as Kaprekar's Constant and this process is known as Kaprekar's Routine.