The Curious Case of the Kaprekar Constant - A Mathematical Essay

Abstract

Kaprekar's routine is a mathematical process that involves iteratively sorting the digits of a number in ascending and descending order, subtracting the smaller number from the larger one, and repeating the process until a fixed point, known as Kaprekar constant, is reached. This essay explores the properties of Kaprekar's routine, its convergence behavior for different digit lengths, and the discovery of Kaprekar constants such as 6174 for four-digit numbers. A computational approach using Python is presented to analyze systematically the routine for 1 to 9-digit numbers, identifying constants and cycles.