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.

Author Bio

Robert W. Ellis is currently a Graduate Teaching Assistant at the University of Tennessee, where he is pursuing a Masters Degree in Statistics. After completion of this degree, he plans to seek employment in the industrial setting before pursuing a Ph.D. in Statistics. This research project became a fascination of his during a junior-level seminar class taught by Dr. Anant Godbole, the chair of the Department of Mathematics at East Tennessee State University, where he earned a Bachelor of Arts Degree in Foreign Languages in 2001. Parts of this research were presented in April 2001 at Appalachian State University in Boone, North Carolina, at the Sixth Annual North Carolina Mini-Conference on Graph Theory, Combinatorics, and Computing.

Jason R. Lewis is currently a graduate student pursuing a Masters of Science degree in Mathematical Sciences from East Tennessee State University (ETSU), where he also earned his Bachelors of Science Degree in Mathematical Science. He began this research while enrolled in a junior-level seminar class taught by Dr. Anant Godbole at ETSU. After finding this problem intriguing, he enrolled in an independent study class over the summer to further investigate the topic. Jason�s plans for the future include continuing his graduate studies in mathematics at the University of Georgia and earning a Doctoral Degree in Mathematics. After completing his education, Jason will seek employment in government service, preferably at the National Security Agency.