Kaprekar's routine

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In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a four-digit random number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in base 10: 9981 – 1899 = 8082 8820 – 288 = 8532 8532 – 2358 = 6174 7641 – 1467 = 6174 6174, known as Kaprekar's constant, is a fixed point of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. The algorithm runs on any natural number in any given number base.

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