6174

The number 6174, or Kaprekar’s, constant is interesting.

It will automatically show up when you do the following:

1. Take a four digit number with at least two different digits (allowing leading zeros).

2. Arrange the digits descending and ascending to two four digit numbers. Add leading zeros is required.

3. Subtract the smaller number from the bigger number.

4. Repeat from the second step.

If you do this a repeated number of times, you will come to 6174 in at most 7 iterations. From 6174 there is no way out.

Let’s e.g. take 8664.

8664 - 4668 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174
7641 - 1467 = 6174