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Article #2720Re: 196 Palindrome Quest, Most Delayed Palindromic Number
From: Edgar De Blieck
Date: Fri, 28 Jun 2002 22:34
Date: Fri, 28 Jun 2002 22:34
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4327 bytes
"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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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 10ff4b,6eabd8191fad2ef6 X-Google-Attributes: gid10ff4b,public X-Google-Thread: 10b299,6eabd8191fad2ef6 X-Google-Attributes: gid10b299,public X-Google-Thread: fe825,6eabd8191fad2ef6 X-Google-Attributes: gidfe825,public X-Google-Thread: 109d8a,6eabd8191fad2ef6 X-Google-Attributes: gid109d8a,public X-Google-Thread: fe885,6eabd8191fad2ef6 X-Google-Attributes: gidfe885,public X-Google-ArrivalTime: 2002-06-28 15:35:30 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!btnet-peer1!btnet-feed5!btnet!news.btopenworld.com!not-for-mail 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 Lines: 73 Message-ID: <afio9p$mm3$1@helle.btinternet.com> References: <67828976.0206281254.105dc051@posting.google.com> NNTP-Posting-Host: host213-122-200-159.in-addr.btopenworld.com X-Trace: helle.btinternet.com 1025303674 23235 213.122.200.159 (28 Jun 2002 22:34:34 GMT) X-Complaints-To: news-complaints@lists.btinternet.com NNTP-Posting-Date: Fri, 28 Jun 2002 22:34:34 +0000 (UTC) X-Newsreader: Microsoft Outlook Express 6.00.2600.0000 X-MSMail-Priority: Normal X-Priority: 3 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000