How To Turn Numbers Into Palindromic Numbers

Still on the subject of palindromic numbers (See http://raffysaldana.blogspot.com/2007/08/palindromes-and-palindromic-numbers.html):

A palindrome is a word that's the same read either forward or backward, such as "rotor" or "tenet". Palindromic numbers, like 22 and 12321, have the same digits forward and backward.

Do you know that most numbers can be converted into palindromic numbers? How? Here is an answer (source: http://mathforum.org/dr.math/faq/faq.number.glossary.html )


"1. Pick a number.
2. Reverse its digits.
3. Add them together.
4. Repeat the process until you get a palindromic number.

Example:

1) 19
2) 91
3) 110
4) 011
5) 121

Nobody knows whether or not this works for every number. People have used computers to try the flip-and-add process on 196 nearly ten million times, without finding a palindrome-- but it might still be possible. We do know that it won't work for every number written in every base: Try 10110 in base 2."

Try this, it's fun :) { Challenge: Can you turn this into a theorem? }

Cheers,

Raffy
8/17/07 in Quezon City