6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:
1. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
The above process, known as Kaprekar's routine, will always reach 6174 in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:
5432 – 2345 = 3087
The only four-digit numbers for which Kaperkar's routine does not reach 6174 are repdigits such as 1111, which give the result 0 after a single iteration. All other four-digits numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4:
2111 – 1112 = 0999
9831 reaches 6174 after 7 iterations:
9831 – 1389 = 8442
Note that in each iteration of Kaprekar's routine, the two numbers being subtracted one from the other have the same digit sum and hence the same remainder modulo 9. Therefore the result of each iteration of Keprekar's routine is a multiple of 9.
495 acts as a Kaprekar constant for three-digit numbers.
* Collatz conjecture
1. ^ Mysterious number 6174
* Mysterious Number 6174 Article