The general approach

For obtaining Kaprekar's Constant, for any digits, there ought to be some general approach. The best approach is that we first assume such a constant exists. Then, we either prove or disprove our assumption with valid results. So, point wise, it should be something like this:

1) Take a number of that digit

2) Try to obtain the subtracted form expressed in unit's digit, ten's digit form

3) Equate the previous number with this number(since our assumption is that such a constant exists). We will obtain various cases:

a. If none of them satisfies, then there is no such constant.
b. If only one of them satisfies then there is an unique constant.
c. If there is more than one cases holding simultaneously, then there are more than one Kaprekar's Constants.

I will illustrate details of obtaining the Kaprekar's Constant for two-digit, three-digit and four digit numbers, as examples of the above technique...