A lot of people who have favorite numbers would likely tell you that their’s is π, or e, or φ, or 27 or 4… ad infinitum. Personally, my favorite number is 6174, also know as Kaprekar’s constant. What makes this number interesting is by the eponymous algorithm; Kaprekar’s algorithm. This is a process by which any number with a number of unique digits equal to its total number of digits can be recurrently manipulated to eventually and always return 6174.
- Choose any number with up to four digits and four unique digits. (1234)
- Rearrange that number twice, once from greatest digits to lowest digits and again backwards (4321 & 1234)
- Take the difference (3087, this is also why you need at least two unique digits. using a number like 2222 just hits zero and the algorithm stops.)
- Repeat steps 1-3 until you reach 6174.
- Repeat steps 1-4 once.
Continuing the process for the initial number returns 1234, 3087, 8532, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174… for most numbers this won’t take more than seven iterations.
I just really think this is a neat number. It isn’t as practical as π, e or 27… but it certainly instills wonder. This works with other numbers of digits too. A few of them are 495, 6174, 549945 and 631764.
D.R. Kaprekar was rather interesting himself. He was a “recreational mathematician” who had no postgraduate training in mathematics and spent most of his life teaching grade school. Kaprekar developed descriptions for several classes of natural numbers. He considered himself a recreational mathematician. He never set out to prove hard mathematical laws or theories; he just wanted to have fun doing math! It just goes to show that Math isn’t all hard work.