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Article #2720

Re: 196 Palindrome Quest, Most Delayed Palindromic Number

#2720
From: Edgar De Blieck
Date: Fri, 28 Jun 2002 22:34
71 lines
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"Jason Doucette" <JasonADoucette@hotmail.com> wrote in message
news:67828976.0206281254.105dc051@posting.google.com...
> Hi everyone,
>
> Recently, one of my emails regarding these quests (in the message
> title) got posted on a newsgroup (which I did not know would happen)
> and I thought it would be a good idea to give a current update of
> these quests, and a short description of both for those who have never
> heard about them.
>
> 196 Palindrome Quest:
> ---------------------
>
> Most people have heard about the 196 Palindrome Quest (or the 196
> Algorithm, as some people call it) via Reversal-Addition.  It arrives
> from a process explained in a 1984 issue of Scientific American:
>
> 1. Pick a number.
> 2. Reverse its digits and add this value to the original number.
> 3. If this is not a palindrome, repeat the process.
>
> It was conjectured that all numbers would eventually produce
> palindromes this way, but 196 is the first number that does not appear
> to do so.
>
> I have personally taken the 196 Palindrome Quest to 13,000,000 digits:
> http://www.jasondoucette.com/worldrecords.html
>
> I have since passed on my record to Wade VanLandingham, and he has
> continued the Quest to over 30,000,000 digits!
> http://www.p196.org/
>
> Most Delayed Palindromic Number:
> --------------------------------
>
> With the same process as above, most people have heard about the
> strange case of number 89.  It takes 24 iterations to become a
> palindrome:
> http://www.jasondoucette.com/cgi-bin/pal.cgi?89
>
> I hold the current world record for the number that takes the longest
> number of steps to produce a palindrome.  It is a 15 digit number:
> 100,120,849,299,260
> It takes 201 iterations to produce a 92 digit long number:
> http://www.jasondoucette.com/cgi-bin/pal.cgi?100120849299260
>
> I have solved numerous other numbers that solve in many more steps
> than 24.  You can view these results on my website:
> http://www.jasondoucette.com/worldrecords.html
>
> Common Mistakes:
> ----------------
>
> 99% of the web pages on the Internet regarding the 196 Palindrome
> Quest believe that 196 is the only number that does not solve out (or
> the only number under 10,000 that does not solve out).  This is not
> true.  Obviously, 691 (196 reversed), or 295 (the outer digits equal
> the same sum: 1+6 = 2+5) both do not solve out either, because after
> the first iteration of these numbers, they all result in the same sum
> as 196 does after one iteration: 887 (and thus, 887 never solves out,
> either, since it is the second step of the 196 sequence).  Find more
> about Lychrel numbers (numbers that do not solve out via
> reversal-addition) on Wade's pages:
> http://www.p196.org/
>
>

Weird! Thanks Jason!

EDEBEDE
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From: "Edgar De Blieck" <Deblieck@btopenworld.com>
Newsgroups: rec.puzzles,sci.math,relcom.rec.puzzles,aus.talk.ltuae,comp.programming.contests
Subject: Re: 196 Palindrome Quest, Most Delayed Palindromic Number
Date: Fri, 28 Jun 2002 22:34:34 +0000 (UTC)
Organization: BT Openworld
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