Thursday, 11 September 2008

Kaprekar Numbers: Kinda cool and totally useless*

*not totally useless, I guess. Please, if you're a mathematician, don't send me angry letters.

I like math. I don't write alot (re: ever) about math, but I find it absolutely fascinating. As a mathematics layman who loves trivia, I get a kick out of mathematical "oddities" and neat little patterns - things that seem to have little practical value but are interesting nonetheless.

One math fact that I'm particularly fond of are called Kaprekar numbers. They can be defined as follows:

Take a number, a with n number of digits. Square a and write out the result. Add the right n digits to the left n (if it's even) or n-1 (if it's odd) digits. If the sum is a, then a is called a Kaprekar number.

For example: 703 is a Kaprekar number.
703 has 3 digits (n = 3)
7032= 494209
494 (the right n digits) + 209 (the left n digits) = 703

The largest Kaprekar number I can find after a very rudimentary search is 533170. I haven't the capacity for math to work out any numbers larger than that.

Also, I really don't know if determining Kaprekar numbers has any sort of practical relevance. Perhaps some mathematician out there could shed some light on them.