Math behind themysterious number 6174

Abstract

At first glance, the number 6174 looks like any other number plucked from thin air. Perhaps this is what makes this unassuming number so remarkable. In 1949, Indian mathematician D. R. Kaprekar, discovered the mysterious beauty of 6174 after devising a process that we now know as Kaprekar’soperation.Themain goal of this research article is to chase the mysterybehind the fourth order Kaprekar constant 6174 using the fundamental principles of Combinatorics and Linear Algebra and to hunt the other ordered Kaprekar constants. Kaprekarconstant 6174 has been an interesting one with its own mystery for decades in the research field of Analytical Number Theory. Many recreational and experimental Mathematicians have been studying this number for decades. In this research paper an attempt has been made to trace the mystery behind that Kaprekar constant 6174 and other Kaprekar constants of all orders. The method discussed here ensures a way to trace Kaprekar constants of any order. Furthermore the proof of the existence and uniqueness of third order Kaprekar constant has been proposed and this proof can be implemented to find the Kaprekar constants of any order if they exist.