Investigations into the Kaprekar Process
Abstract
Robert W. Ellis and Jason R. Lewis
D.R. Kaprekar discovered an interesting phenomenon that occurs when one takes a
four-digit number, such that all four digits are not equal, and computes the difference
between its decreasing and increasing rearrangements. He found that within seven iterations
of this process you will always reach the number 6174, and this process became known as the
Kaprekar Process. In this paper we decided to investigate the results of the application of the
Kaprekar Process to numbers of various digit lengths. This investigation includes new
information about the Kaprekar Process, such as a statistical analysis of the Kaprekar Process
on four-digit and five-digit numbers, and a description of the relationships between different
four-digit numbers after the application of the Kaprekar Process. We also provide a summary
of the results of the Kaprekar Process when applied to various digit lengths, and a look at the
palindromic sequences which present themselves in this investigation.