KAPREKAR'S Constant

Interesting mathematical fact: *KAPREKAR'S Constant*

The number 6174 is really a mysterious one. At first glance, it might not seem so. But as we see, anyone who can subtract can uncover the mystery that makes 6174 so special. To begin with, choose a four digit number, where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can form. Then subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number. Eventually, you will obtain the number 6174. Thereafter you will keep on obtaining same number. It is a simple operation.

Let's try it out, starting with the number 2016. The maximum number we can make with these digits is 6210, and the minimum is 0126 or 126 . The subtraction steps would be:

6210 - 0126 = 6084 *****
8640 - 0468 = 8172 *****
8721 - 1278 = 7443 *****
7443 - 3447 = 3996 *****
9963 - 3699 = 6264 *****
6642 - 2466 = 4176 *****
7641 - 1467 = 6174 *****

Once you reach 6174 the operation repeats itself, returning 6174 every time. Thus the number 6174 is a kernel of this operation.

Let's try again starting with a different number, say 1789.

9871 - 1789 = 8082 *****
8820 - 0288 = 8532 *****
8532 - 2358 = 6174 *****

We reached 6174 again!

One reaches the kernel in maximum seven steps.

This is the famous "Kaprekar's operation".

In 1949 the mathematician, D.R. Kaprekar from Deolali, India, devised this process, now known as Kaprekar's operation.

The number 6174 is also known as Kaprekar's constant.