# Every Number is the Sum of Three Palindromes - Numberphile

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- Published on Sep 17, 2018
- Featuring James Grime... Check out Brilliant (and get 20% off their premium service): brilliant.org/numberphile (sponsor)

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More James Grime videos on Numberphile: bit.ly/grimevideos

Main paper he discusses: arxiv.org/abs/1602.06208v2

And the base 2, 3, 4 paper: arxiv.org/abs/1706.10206

Website by Christian Lawson-Perfect to run the algorithm: somethingorotherwhatever.com/sum-of-3-palindromes/

Applet for any base 5-10 by paper author Lewis Baxter: www.rnta.eu/cgi-bin/three_palindromes/pal3.py

Lychrel numbers: ru-clip.com/video/bN8PE3eljdA/video.html

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outreach/science-sandbox/

And support from Math For America - www.mathforamerica.org/

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mienzillazDay agoJames, you should make custom font with your handwriting, i would be first to download..:)

Amanda qeqqaqig14 days agoWow

Chris DohertyMonth agoThere's absolutely loads of ways of deconstructing every number. This is the 100th way I found for 3141592 with a brute force type algorithm I wrote.

(3088803, 47674, 5115)

Brian Dennehy2 months ago^{+1}This is amazing

Mr. H2 months agoAnd these are unique palindrome numbers?

Navodit Chaudhary2 months agoSetters at Google used the paper to create a Google code jam final problem

RASHO IE'TOLAN3 months agoBeautiful as *fooooooook*

🤩🤩🤩

Rabbit the One3 months agoNot looking so well in this video Grimes. Have you had enough sleep lately?

Ahmed Elian4 months agoBut are the three palindromes a unique solution?

Henrik Soderstrom4 months agoIs the solution unique or not?

Maxon Mendel4 months agoJames needs a new phone

Zachary Perkins4 months agoi wrote a program that just goes through all the combinations of 3 palindrome numbers. the palindrome numbers are just generated up to the number you want, and then checking if they're the same backwards. They have a lot of possible combinations. 3141592 has 3112 (which is funnily also a palindrome) 3 number palindrome sums

DaveDonnie4 months agosuduku

Thiago Soares Leite4 months agoWhy Just positives?

If you multiply every palindrome by -1. You ter "ALL negatives integers" or Did I missing something?

tully balcom4 months agoThe carries are also palindromic.

Raoul Gerrits4 months ago9:00 even the carry count is a palindrome, neat

Christian Herenz5 months agoWould be fun if you have the authors on your show ... Seems they've been working on Palindromes also in different context.

Brandon Brimer6 months agoIt's probably been called out already but the carried numbers form a palindrome as well. Math is amazing!!!

rate eightx6 months agoBut What Three Palindromes Do You Use For, Say, 1? Or 2?

kaushik mitra6 months agoIs he wearing a skull cap

Jivan Scarano6 months agoIs one of the palindromes allowed to be 0? If not, how do you solve for 1 or 2?

Jivan Scarano6 months agoGauss has the same birthday as Kirsten Dunst… and me.

Nevaeh Anglique6 months agoI had a question that asked what three palindromes made up I think it was 2014?? on an old math competition problem set we were using for practice

debblez6 months ago^{+1}or you could just...

3141413

+ 171

+ 8

_________

3141592

“small” numbers don’t require algorithms...

nunyabiznasty6 months agoYour solution indeed works as a possible solution in Base 10, but the algorithm described in the paper also has to work in _literally every other base, no matter what._ It therefore has to respect quite a lot of special cases, especially when we are talking about palindromic numbers in odd bases such as 3 or 5, as mathematical operations involving digit manipulation (such as palindrome addition) can become quite funky if you're not careful and there are in many cases no "small" number solutions for these bases. (On a side note, this property of smaller bases is, if I understood the paper correctly, one of the reasons why there was this one rule mentioned by James in his demonstration that the categories are partially based on what the first digit of the target number is). Due to these cases, the resulting algorithm becomes more complicated, until it eventually becomes convoluted enough that it produces vastly less intuitive results even if it is, as you have proven, possible to generate a much smaller, quicker valid solution (at least in base 10).

Tony Coleby7 months agoOne of the more amazing videos.

Chick3nWings 3457 months agoAny 1 digit number is easy

Mayor Video7 months ago11 is a prime number which means I can't split equally, I am a palindrome, two ones to call my ownnnnn

hgam7 months agoi can think of an easier way than the methods in the video: first you identify the type of the number and fill in the first and last digits, then you subtract the 3 numbers you get from this step. For example, for 3141592 in the video, you subtract it by 2000002, 900009 and 10001 and get 231580. you then delete the zero from the end and get 23158. this number will follow the same property as it can be put into 3 palindromes, which are the middle part of the answer for 3141592. then you can identify the type of number this is and carry on.

KamuiSeph7 months agoSuDUHku?

Guys... It's SuDOHku.

KasabianFan445 months agoPipe down, James corrected himself a few seconds later.

Kiki Kikison8 months agoThe "carry" line was also a palindrome.

TeserT8 months agoPi is there 3141592

שחר א.8 months ago9700079

0322223 +

0099699

---------------

MY BIRTHDAY -> ME!!!

brendan edmonds8 months agoWhat about 1?

Rodrigo Watzl8 months agoAbout sudoku: consider a 9x9 square board of sudoku. It contains nine 3x3 boards inside. How many possible ways are there to complete the intire board?

Jack Scrivens8 months agobut you do it with 1?

TruthNerds8 months agoThe website rejects any input >2^128-2^104+2^74. Don't ask me how I know that.

Jako19878 months agoSaippuakauppias

Innostunut sonni

Saat Atte satasetta taas

Palindromes are cool

Mujahid Syed9 months ago5:55 "Soduko"?! It's pronounced "Sudoku". Plz, it really irks me when people do that. Nice vid btw.

Ben Heideveld9 months agoHow many different ways are there to write numbers as sums of three palindrome numbers? (on average, minimum, maximum)

zebracherub9 months ago^{+1}For a given number, we could write down all the possible palindromes it is made of then, right?

J K9 months agoI’m upset

Ian Moore9 months ago^{+1}does this algorithm generate the smallest possible combination of palindromes, or is there anything fancy and interesting about their distribution? Highly intriguing!

C21H22 N2O29 months ago^{+1}Is it possible that every number is the sum of three palindromes, while the carrier numbers together are a palindrome too?

Luke Gabriel Balgan10 months ago^{+5}But how do you memorize so many algorithms for each individual special case??

sees rubik's cube

*oh...*

mirage in the desert10 months ago111+222+333=666

mirage in the desert10 months agoSo every palindrome can be written as the sun of three palindromes

Damien Mitchell10 months agoThe website says that 12345654321 would equal 12345654321+0+0. I'm unsure if that's considered adding 3 palindromes together.

Glen Gerod10 months agoI didn't realize that Johnny Lydon did maths.

venkat34710 months agoSum of palindromes for 1 please

Ratzler11 months agoThank you for providing me with a new and fun way to fill up my spare time, I'll just go print out those *40 pages*

Pinto11 months ago^{+1}Virgin level 200

RLB11 months agoMy name is Reinier which is a palindrome. I thought I should mention that. Bob, Anna and me sum up to Brady's birthday.

Billy Bob Thorton11 months ago^{+2}Some guy: Man I with their was a way I could figure out the three palindromes that summed produce this number.

Some other guy: there's an app for that... Also why?

Sam Parfitt11 months agoI bet the website now knows all of our birth dates..

macleadg11 months agoIs this video the same when viewed backwards?

Jarom AllenYear agoWhat if your integer is less than 3? How can, say, 2 be a sum of 3 palindromes?

Raluca ButaYear agowhy do we have only 9 numbers really ? Who invented the number system ?

JoeYear agohere i was thinking i was gonna blow my math teachers mind....

ionisator idkYear ago^{+1}77777777777

7+7+7+7+7+7+7+7+7+7+7

7 times eleven equals 77.

7 plus 7 equals 14.

14:2 = 7

Booom.

Stephan JancarYear agoWhat about 10420275