The Kaprekar constant in a given base is a -digit number such that subjecting any other -digit number (except the repunit and numbers with repeated digits) to the following process:

1. Arrange the digits of in ascending order, forming the -digit number , and then in descending order, forming the -digit number .

2. If , calculate ; otherwise .

3. Goto step 1 using instead of .

eventually gives . (This process is sometimes called the Kaprekar routine).

For , the Kaprekar constant for is 6174. Using , we find that 9721 - 1279 gives 8442. Then 8442 - 2448 = 5994. Then 9954 - 4599 gives 5355. Then 5553 - 3555 gives 1998. Then 9981 - 1899 gives 8082. Then 8820 - 288 gives 8532. Then 8532 - 2538 finally gives 6174. (Some numbers take longer than others). and don't exist for .