A fascinating observation!!

When we take a number, any digit number...say 1234, we will always obtain a greatest and a least number possible by rearranging the digits of the number(here the greatest possible number will be 4321 and the least possible number will be 1234). For numbers with all equal digits we will obtain the same greatest and least number. In this discussion, we will show interest to only those numbers which have discrete possible greatest and least numbers by the permutation of their digits.

Suppose, we subtract the least possible number from the greatest possible number in the previous case, i.e.

4321 - 1234 = 3087

Now, for this new number, we run the previous technique to obtain a greatest and a least possible number. They are 8730 and 378 respectively. So we subtract them again, and continue the process further.

8730 - 378 = 8352
8532 - 2358 = 6174
7641 - 1467 = 6174!!

And the process suddenly terminates! However we may try to proceed further, the number 6174 will always generate 6174 again....amazing, but true. This stunning phenomenon was observed by the famous mathematician D.R. Kaprekar and so the constant 6174 has been named as Kaprekar's Constant.

One thing to be noted, that is, 6174 is not the only Kaprekar's constant. It certainly is the only Kaprekar's constant possible for four digit numbers. For three digit numbers this constant is found to be 495. For all digits, Kaprekar's Constant isn't found. Instead a cycling series of numbers are obtained(e.g. for two digit numbers), again in some other cases, we obtain more than one discrete constants.

For more details, visit Kaprekar's Constant from Wikipedia, the free Encyclopedia.