ebabe

Cheap whiskey and palindromey stuff don't mix. Especially when palindroming numbers because palindroming numbers involves high math, i.e. addition.

There are only two kinds of palindromes; (1) words that read the same from left to right as they do from right to left, and (2) single numbers that total the same amount when the digits are inversed, and (3) when both numbers and letters can be inversed without altering the meaning of each. (I don't count #3)

But anyway, my palindrome "ebabe" (24,000 google hits) numbers "52125" if each letter is assigned its relative position in the progressive numbering of our alphabet. Of course all palindromic words are palindromic numbers, but this one serves well as a handy challange to find the root number for the palindrome.

But it won't be easy. I'll bet my bottom dollar that there is not a "ebabe" in the house who can find that elusive number.
Neither have I...yet, but I'll bet you my other bottom dollar that I can...can you? Go!
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Some interesting facts: What is a Palindrome?

A palindrome is something that reads the same forward as it does backward. It originated in the early 17th century from the Greek word palindromos (palíndromos), literally meaning "running back again."

Numbers: "52125", "4334", "8", and "1758571".
Words: "Radar", "I", "Eve", "Deed", and the world's longest in the English language: "Redivider".
"Madam, I'm Adam", and the timeless classic: "A man, a plan, a canal... Panama".

Numeric Palindromes: Here's the algorithm:

1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, go back to step 2 and repeat.

Do all numbers eventually become palindromes by this process? It was suggested that this is the case but it hasn't been proven.

Most numbers become palindromes fairly quickly, in only a couple of steps:

13 -- 13 + 31 = 44 (one step)

64 -- 64 + 46 = 110 then 110 + 011 = 121 (two steps)

87 -- 87 + 78 = 165 then 165 + 561 = 726 then 726 + 627 = 1353 then 1353 + 3531 = 4884 (four steps)

In fact, about 80% of all numbers under 10,000 solve in 4 or less steps. About 90% solve in 7 steps or less. A rare case, number 89, takes 24 iterations to become a palindrome. It takes the most steps of any number under 10,000 that has been resolved into a palindrome. But the number 196 has not yet been found to result in a palindrome even after 40,000,000 steps of inversions and additions that led to a number with 600,000,000 digits.

Last edited by themilum; 11/21/05 02:29 AM.