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.

Daniel,

When I saw this post I thought … I think some time in the past I wrote a PreAlgPoW on this topic. Sure enough, I found it!

The Magic of Number 6174 [Problem #1730]

If you’ve not seen it yet, you might enjoy reading the Solution and Commentary to see how kids approached the problem:

http://mathforum.org/pows/solution.htm?publication=1060

~Suzanne