Kaprekar's constant

Kaprekar's constant is arrived at by following these steps:

1. Take any four-digit number whose digits are not all the same (leading zeroes are allowed).
2. Sort the digits in descending then ascending order, making the largest and smallest possible 4-digit numbers composed of those digits. (Add leading zeroes if necessary.)
3. Subtract the smaller number from the larger number. The result will be another 4-digit number.
4. Repeat the process starting with the result.

For example, starting with the digits 0827 (today's date) we get:

8720 - 0278 = 8442
8442 - 2448 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174

If we continue the process outlined above the result will always be 6174.

7641 - 1467 = 6174

The amazing thing is that starting with any 4-digit number whose digits are not all the same will result in 6174 in at most seven steps. 6174 is called the Kaprekar constant for 4-digit numbers after Dattaraya Ramchandra Kaprekar who discovered the property in 1949.

There's a Kaprekar constant for 3-digit numbers as well. Following the same procedure above starting with any 3-digit number whose digits are not all the same will end in the result of 495 in at most six steps. Applying the same process to base 10 numbers with any other number of digits will result in either zero or a cycle that never ends. (Check out the article Mysterious number 6174 by Yutaka Nishiyama for the proof.)

You can see the results of the Kaprekar routine for 3-digit or 4-digit numbers using the utility below. Just enter a number in the first field and click the "Calculate" button. The results will appear below.