What's special about 196?

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Dr James Grime delves into the largely unresolved world of Lychrel Numbers?
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[@AmronFortis]

I just love to hear this guy talk about Noombahs

[@reylancedispo822]

HAHAHAHAH noombahs

[@dyhrbergdk9541]

I continued to say it out loud while peeing after the video. "Nummmbah".

[@NuisanceMan]

"Noombah noomhumbug," said Ebenezer Noomscrooge.

[@RedRad1990]

Whoos yo favoree noombah, Breadee?

[@FanTazTiCxD]

nØmba

[@TheSugarDealers]

"Give me a two digit nummmmbaaah."

[@justinthomas7222]

GIVE ME THA MEETAH! Whoops, wrong channel!

[@asmaakram3299]

Lol

[@SreenikethanI]

@@justinthomas7222 oh em jee oh em jee doubleyoo tee yeff!!!

[@8-bitfox716]

14

[@RevolutionibusOrbiumCoelestium]

23 😊

[@suave319]

"Numbah" XD I love him :P

[@IceMetalPunk]

+Suave Atore Lots of planets have a north :P

[@emre1929]

ahahahahhha numbah :D

[@ConulaxHD]

i love british accent haha

[@ElShogoso]

+Suave Atore A legitimate numbahphile video.

[@mattiassollerman]

+Suave Atore "lonnngah nummmbah"

[@ragnkja]

Either all of 196, 295, 394, 493, 592, 691 and 790 are Lychrel numbers, or none of them are. This is because all iterations after the first one are the same. (Note how the middle digit, as well as the sum of the first and last digit, is the same in all these cases.)

[@freedom13245]

they're all in the form "a9b" where a+b=7

[@effortless35]

+Nillie Is there a Lyschrel number candidate that doesn't end up on the same sequence?

[@ragnkja]

effortless35 Yes. The smallest of those is 879.

[@Martmists]

+Nillie no, the smallest is 689

[@effortless35]

Nillie So how do we know that it doesn't give the same number after 20 trillion steps as 196?

[@thewanderers97]

I love how there are serious comments from years ago mixed with r/196 shitpost comments

[@snekofspice8139]

when the floppa is based 😳

[@doubleoof7907]

Based

[@yeepyorp]

literally 196

[@iamnotafederalagent5552]

196 is dogshit

[@thewanderers97]

@@iamnotafederalagent5552 yes, and? That applies to literally anywhere on reddit

[@HYEOL]

196 is the only number with a 1 a 9 and a 6, in that order, and without any other numbers

[@MrFlameRad]

.196 1.96 19.6

[@HYEOL]

1E+96 ? XD

[@ProfessorSyndicateFranklai]

*natural

[@PaddedShaman]

HYEOL If you write 258 in base-12, it's 196

[@penultimatechimera7981]

196196

[@thomaspaine5601]

This is like Sesame Street for adults. Today Numberphile is brought to by the number 196.

[@numberphile]

If you'd like to support Numberphile (and get a limited edition Brady-signed postcard from this video sent straight to your house) --- here you go: www.bradyharanblog.com/postcard/89

[@victorvescu]

+Numberphile Hi, Brady! I would definitely get a postcard is they wouldn't be so pricey... :( 20 pounds is not how much I can convince my parents to spend on a postcard, despite being it signed by someone I am a fan of. I would love to see some cheaper postcards in the future, maybe some Hello Internet postcards, who knows. A student from Romania.

[@numberphile]

+VICTOR VESCU I understand Victor - this little thing is really way a to raise some extra money for video animations and it's surprisingly time consuming (when I should be making videos) to personally write and post them all! Have you seen the Numberphile posters? Because someone else helps with all that and they are not a limited edition, they are much cheaper at just $9 (and much bigger than a postcard!!!) store.dftba.com/products/numberphile-poster

[@KainYusanagi]

+Numberphile YAY! These are the sorts of videos I subbed for. More of these please!

[@mjoto]

+Numberphile The building # I work in.

[@LynneSkysong]

+Numberphile I'm glad I saw the e-mail this morning. I grabbed one of your lovely postcards (probably less lovely, but with a story to tell after it arrives) and my order was number 22. Already a palindrome, but also meaning (if my assumption is correct) that 21 postcards had already been sold in that timeframe. They're going quick!

[@milkyJuman]

Number rule

[@NSViewController]

May /r/195 rest in piece

[@finnishboy5923]

Praise Floppa, Remember r/195, and Post before leaving

[@lukesimonsen3002]

Fanter

[@Jequetepeq]

Floppa friday rn

[@bogusWasHere]

make sure you comment before leaving the video, it’s the rule

[@bird-war]

Huh, that's quite funny! It's making the rounds on the Internet

[@Hyblup]

:o it’s the number guys, you know what _that_ means… rule

[@chriswatson4679]

I noticed, that the Lychrell numbers you listed as possible are also palindromes in some pairs, 196, 691; 295, 592; 394, 493; etc. Also, they all have an even at one end and an odd at the other, with 9 in the middle.

[@user-ds8ug8eb2i]

Be sure to follow the rule before you head out.

[@settrasurfs1780]

RIP 196

[@shosad5934]

:(

[@hahnwill0947]

:(

[@CuldirOfficial]

rip bozo

[@PhadexLXIV_Greece]

196 pack going hard🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬🚬

[@mccookies3664]

where is the communist femboy floppa

[@doubleoof7907]

Literally 1984

[@GarTheFish]

Big Floppa.

[@phoenixchase9271]

Praise floppa! Only 2 days until floppa friday

[@scott.s.3356]

Fanter

[@jacobroberts44]

Rule 1: You must post before you leave.

[@robbery666.]

real

[@coolbeans3635]

rule femboy big floppa

[@drdappertopper4506]

rule

[@kode_2005]

Rule

[@xenuvelo64]

fanter

[@Sueci]

True

[@venz0h420]

floppa friday

[@epicgamernik76]

rule

[@apikobalt]

r/196

[@dankmemes7342]

home of awesome

[@fallingmountain4706]

when the impostor is sus!

[@dwevin]

literal 1984

[@couch_enthusiast8915]

if you know, you know.

[@baako0834]

floppa

[@Anonymous-376]

Love how the Google translated version is "flop"

[@henry5636]

Big floppa rule femboy

[@clifflacausa9280]

89 takes 24 steps and it is the 24th prime. The nature of numbers is beautiful.

[@arminarlert6105]

le funny femboy sub (You must post things before you leave, You must post things before you leave, you can't leave before you post something)

[@jacobroberts44]

goblinhog

[@blakethesnake6686]

make a video about thrembo

[@maggy154]

THREMBO IS NOT REAL ITS NOT A REAL NUMBER TAKE YOUR NORMAL PILLS

[@stellasdoesstuff]

as soon as I saw the title, I thought 14^2

[@100skalps]

+Stella Marie So did I. Kindred spirit eh? :)

[@scinorandex]

I memorize 1^2 - 16^2 so yeah

[@Luisitococinero]

Yeah!

[@iamTheSnark]

Yeah. 13^2 and 14^2 are written with the same numbers. 169 and 196.

[@victorbeidiljohnsen5257]

Me too

[@OatmealGrillBlazer]

r/196 gang rise up 🏳️‍🌈

[@gabagoooby]

196 is a trash sub

[@theidioticbgilson1466]

@@gabagoooby reddit is a trash website

[@General12th]

@@theidioticbgilson1466 The Internet is a trash communication method.

[@theidioticbgilson1466]

@@General12th communication is trash reject language return to picking parasites off ya homie's back to form emotional bonds

[@RichConnerGMN]

@@theidioticbgilson1466 omg is that mitch halley

[@philiphanhurst2655]

rule floppa fanter ionic pillar

[@blackbacon08]

Cringe ionic coomer

[@doubleoof7907]

Corinthian Supremacy

[@Ðogecoin]

RULE

[@pegy6384]

Yay! Dr. Grime's notes finally get some camera time! I'm always curious about what he has worked out and has at hand before you begin filming. I like seeing little details like that.

[@ColinLim0721]

Thank you Brady and all of the professors for making these videos!

[@axbs4863]

You should do one about (literally) 1984 next

[@jackwalsh8601]

does this mean that if 196 is lychrel all of the iterations of it are lychrel e.g 887

[@TheMaginor]

+Jack Walsh yes

[@jackwalsh8601]

I was thinking that. Someone can now prove that there are infinitely many Larshel numbers if one number can be proven to be Larshel

[@lolatomroflsinnlos]

+Jack Walsh Logically, yes.

[@effortless35]

+Jack Walsh Yes, but then we can ask whether there are distinct sequences or all Lychrel numbers must end up on the same path eventually.

[@toast_recon]

+effortless35 Great observation. Nothing about this process really seemed interesting to me before now, but now I'm curious. Maybe you'd end up mapping it, with "lychrel nodes" in a "lychrel network". So cool.

[@TheNunoTubes]

Honestly, I'm a bad math student and even though I understand its importance and significance in science and our world, I've never really shown any interest for it. But I really like watching this guy, just the his enthusiasm about numbers and the way he teaches it had me subbed. Plus it's always cool to learn little things like these.

[@hakkbak]

it's not really important in science. Because this is just playng around with the properties of the base-10 convention that we use: convention doesn't, in most cases, bring about revolutionary discoveries.

[@oO_ox_O]

+adma1987 Linked: James Grime singingbanana

[@effortless35]

+hakkihan tunbak He meant that math in general is important for science. Not this problem in particular.

[@hakkbak]

+effortless35 ah yes you're right. then I agree, math is very important to science.

[@vizestroowash]

+TheNunoTubes Couldn't have said it better myself!

[@NoriMori1992]

3:51 James: [writes 196, 295, 394, 493, 592] Me: Wait, so these are all 99 apart?! James: [writes 689] Me: Aww. James: [writes 691] Me: Ooooh! But I wonder why 689 breaks the pattern?

[@ziquaftynny9285]

+NoriMori Probably something to do with it being in base 10.

[@NoriMori1992]

Ziquafty Nny How so?

[@ziquaftynny9285]

NoriMori Changing it another base ruins the pattern. This entire patterns depends on it being in base 10, along with the break in pattern. The pattern is in it being in base 10. Sorry if I explained badly, I just feel it intuitively.

[@NoriMori1992]

+Ziquafty Nny I still don't get it, but thanks for trying. XD

[@theleftuprightatsoldierfield]

196 + 691 = 887 887 + 788 = 689 + 986

[@johnnicholson4862]

The number served me well, I used it for a theme in a crossword in Magpie (great crossword mag). If you outline cells in a grid using the digits of the number repeatedly, turning 90 degrees clockwise after each digit until returning to the start point, you get a nice windmill shape. Solvers then had to turn the windmill and the letters within it to form palindromes in the grid. (Thematic ish!) I only discovered your channel recently and love it. Thanks very much.

[@cynicrocketjump4071]

Floppa femboy oil hand leftism

[@santiagomahecha8690]

Every day, I live in constant fear of the hand.

[@jacopolattanzio8790]

what

[@santiagomahecha8690]

@@jacopolattanzio8790 r/196

[@apikobalt]

Fantet underthales downloader

[@doubleoof7907]

based

[@Rukalin]

Thought this was gonna be something about it being 14².

[@Luisitococinero]

LOL, that little 2.

[@Rukalin]

+Luis Calderari Well yeah... It's an exponent.

[@groszak1]

@@Luisitococinero ² is a superscript 2

[@aryanjha1]

So you commented on this video 6 years ago huh ? I was wondering if you still use this acc😐

[@Rukalin]

@@aryanjha1 I do

[@yermomLeslie]

When the number is sus! 🧐🧐

[@doubleoof7907]

fanter

[@OatmealGrillBlazer]

floppa

[@peon17]

This is actually one of the problems that originally got me interested in mathematics some 20 years ago. I remember bringing a small notebook around with me doing these calculations by hand when I had a few free minutes.

[@dhbartlett12]

This kind of video is why I subscribed. Thanks Brady

[@epicsomethingstore6691]

where's floppa?

[@jawnpodricque1452]

*proceeds to post before leaving*

[@avigailpekelman8239]

Based

[@rruzgarr97]

Dr.James Grime is my favourite. %50 Numbah %50 Smile at the camera %100 Awesomeness

[@mariomario761]

Honestly, as a Geographile that I am, I thought what was special with 196 is that it's the amount of countries that most experts will tell you there are :P

[@davidvarna]

Ah my favorite subreddit

[@XerTaaL]

full of lgbtqs

[@jorian_meeuse]

Me: isnt that 14 squared? James: hold my brown paper

[@peleg462]

Rula

[@liveordie200]

4:00 "please turn your books to page 394" is immediately what came to mind

[@DepFromDiscord]

*clears throat* SNAPE

[@10mimu]

0:27 I was thinking 23 I'm clairvoyant

[@rogerbradley9449]

+Istari Pallando Same here!

[@112048112048]

+Istari Pallando I also guessed 23. By the way, how's Alatar doing? I haven't heard much from you guys recently.

[@10mimu]

+Roger Bradley I gues there must be some statistical property regarding 23 when guessing two-digit cardinal numbers.

[@10mimu]

+Johan Westin We missed the whole fun :(

[@TheGullimonster]

+Istari Pallando 69 ? ;)

[@ryan_s]

After watching all these numberphile videos, I've found that pretty much all numbers are special.

[@Theo-pd3ny]

People I can hear forever talking with a brit accent: George Harrison, Peter O'Toole and now James Grime. I just love him! :)

[@surenpoudyel8649]

0:42 “let’s see if we can do a bigger numbaaa, maybe it will take a little lungaaa.” 🔥 😂

[@talosgak1236]

Amogus

[@woollypidgeon1948]

ruleé

[@irenec8361]

This is a wonderful video; very intriguing. Mr. Grime it is always a pleasure to watch your videos with Brady at the camera. You have a way of explaining things out without unnecessary complications thrown in simply to 'look smart'; you are and it shows. :)

[@s.b.easwaran7563]

Greetings from India, Dr Grimes, and from a big fan of Numberphile. This video reminds me of the Kaprekar constants 6174 (for four-digit numbers) and 495 (for three-digit numbers), named after a hobby number theorist and maths teacher ( D.R. Kaprekar) who discovered them. I'm sure you know how they work: take any four-digit number and rearrange the digits to make the highest and lowest possible numbers; then subtract the smaller from the larger; repeat, and you'll notice that in seven iterations or less you arrive at 6174. If you use three-digit numbers for the same process, you arrive at 495, again within seven iterations. It doesn't seem there are similar constants for five-, six- or more-digit numbers. Would love to have you present the Kaprekar constants in your own lively, inimitable style--and of course with the mathematical insights you might have about them.

[@sundaranarasimhan58]

I too will like to have a video on it

[@LXNC8]

you guys are doing such a good work. teaching the world and making maths interesting for people like me. you people are doing a great service for the world.

[@jaipod4561]

Fun fact. The name "Lychrel" was coined by Wade Van Landingham as a rough anagram of "Cheryl", which was his girlfriend's first name.

[@pramitbanerjee]

227th view. That's a palindrome in step 1! Palindrome numbers are prevalent in biology, as these are DNA sequences that are often recognized by enzymes such as restriction enzymes(type 2). Although these sequences are quite small. May be we can have some application in biology in the future.

[@Cjnw]

Normie

[@psyachu]

I noticed that the first few of the first Lychrel numbers are only almost 100 off because each set of the number and palindrome add up to the same number. Like, the first digit would increase by 1 and the last digit would decrease by 1, but because they're palindromes, the net difference between the sum of those sets is generally the same.

[@boptillyouflop]

Dude, that process looks like a Turing machine to me! It has an infinite tape! (2 stacks - both ends of the number) It can either loop infinitely or not and we can't seem to prove any rules on when it loops and when it doesn't.

[@tjtommy5495]

Love this comment!

[@settrasurfs1780]

Spronkus Kronkus my beloved

[@brycegutierrez4677]

I love seeing classic numberphile videos like this!

[@octavioserranomusic]

That list of possible lychrel numbahs was interesting and I'm surprised they didn't point this out. 196, 295, 394, 493, 592, 689, 691 1 - they all have 9 as the second digit except for 689 2 - they all have reversed counterparts (196 - 691, etc.), and again the outlier here is 689

[@michaellin4553]

I found out about this first on reading about applying non-lychrel numbers to elliptic curves, to observe OTP properties.

[@ramarromarrone]

I love to see the smile on your face when you explain things.

[@truefregn]

For all of the potential three digit Lynchrel numbers, you will get the same answer, since adding the reversed number to them always gives you 887.

[@sinancalsr726]

i was expecting something like this, 196 is special because it is square of the 14.

[@produck11]

These are the kinds of numberphile videos I love

[@ethernetleum235]

Trans rights floppa femboy pillar hand amogus

[@jakojenhh5002]

pillars

[@MalcolmCooks]

I have found the final iteration of 196 that ends in a palindrome, which the size of this comment is too small to contain :)

[@franzlyonheart4362]

Underrated comment

[@Doge-zb7ku]

Fanter

[@Whyyyyyy]

So this is the first time I've heard about anything special about base 10 other than it being the number of fingers we have, you guys should do a video of interesting facts about base 10!

[@ballz_XLI]

196 🤢🤢🤢

[@LittlePeng9]

Today was a good day, I've learned the pronounciation of "Lychrel" :)

[@rosiefay7283]

I've finally learnt where it comes from.

[@FahlmanCascade]

I'm glad to hear that this problem hasn't only been studied in base 10. It would be a lot less interesting if that was the case.

[@WalterKingstone]

"The numbers are now 600 million digits long" Wow...

[@MABfan11]

*puts it as my password*

[@e1woqf]

@@MABfan11 Easy to remember 😎

[@flopsnail4750]

@@MABfan11 lol

[@theantimatter]

and then you're asked to add a lowercase and an uppercase letter, and a special character.

[@SoumilSahu]

you have among the most informative channels on YT

[@suren6885]

Iteration: ---- 32287 Not a Palindrome : 400398078695418760686908199080144499925832903715045466836604763864192187141650156290277866349290300195214937020603686257034351476521434227312405656609611510831471083252130191154396677893643257839547604308758400504169500975637633669075995041841371959461343932303097903732845735912133211006905095747031710476486328463687030910579535801531326884502465604129498027439610695056042015777601837962553258897251782386446763807799920019922158757596393313230390678129740311263964365396894501385461556449834289560519906298148600459995148180657922664205421687282974793337675390141384817714640753893883610293028069125714976544811512815640702974677801019367971810241358003924251376989603866630450595486193270326066608285102067534413890097999167120966047832267453587379206149382955334936012296494841068357056031956478541115640595454736354052235681610900570665957566040115777800765821324052370784313957021804026861741045095788264243942666631804561031021519077453291251868717135913526126040884260537365042510536988024638172354314878914468561818904244655885388526694089068321407933999938850705979835229751860609558009110022750991368295609458186748928569616408286788558344392536138778535766095862642193233902501530214992932694815021794300389685896788532250224847017143026001960096694548352991362418312431623922456776554866726947756756882919022161682763345810606120656516444857902213388628045660820999592814467105455607974805507277715644908695203564787894503679371530872120786126018282925267762411156713633183346230636940204495234152499747582955028847965137361260248461154589525291771798441942247025620489591956475587639867094922946767823828066017612154667633909875051277753406827996368875255379299467117742330832109517900720778685322274807861048338964178943498666982813753636504041233626396616548420581371019382660076046783347287223324143039116867537906541592236440262005057539653353119521186665381517112685243589622000826869894418332288570435050402301818596479119101376101414332677076115043495773202749413124047336917548293513844128594247922373741616464534779083494419040679165994071750424977065867570886931635473824188841251268385984287858959827325017625197317619911861649729268864623583933269576042291732239638955826641173858004462394134625136894715068136256216350465777822175166828939143829498702823399731488561858689442102199506959467919980323351010228962948517894336491575337372138411287023456591949117741457500378713289320786146688224331842021616017250887165421650185424464059874258398479967807156887799956591162204350058370488976433181704067764149347746526272422019687962670435894423208839685830610870789370333123306589506680296311959458944298591421088796563231265694978720035391363233103358440338797164891472026123479367061265618557999128870231022044889149854221070095544050935164235302615680153895561680619832669167268443153502099518803028574696547355876186362434499185195774297105028713544997890494927080281294909860206255907763958921417966503891274674807834268140103154285916310825361880425720512107143896824594892403729061494234546344563868041034569069357582870699226162525401411485889765479806317556677089653355058737997795394518847802233862063191644699185741719564932638368122623508300807636301726645236518143393378549006456702633552671759158096997789522805303131512432436619033525324122330393129892621973877383529956643765947123161741377693134310437383863906126345648582374844656630311626884171849068860622645442085757354543173802844137886455922614375962325102454450107288936288649292355939878161743931363254996893265334186341528700218990955020322506877259814963033035103902749811376821076546130160843298980366033177058095896107850333632713120530403793357999539741480881870836686926348605120002691996341207139646813121348592740139614352305157582810761416982197869622939800517222465450613302944161702682292583697010410258568505868925978993604475980432324105146480861976959228986728867048167214719916924231348564889749479319610504596992735406100714235543065186437762051937470505335064089957497815974561889127133213238515349218643290978778250988632536895422480626016002800832670184295458195296512572425216353933116364125995199031608100616457468029199705573340228271035796317870497535473842366375801973097230709284193399387164533653845929770118383362407986309866528062304055754821123787589591733766910013614695745440866643067463500499254879366286851908053882209717795847753866225776700255108609610778917751037123901075857741

[@linasuperdina994]

this is the first of his videos im watching. It's kinda cute to see someone get so excited about a number

[@triplev-th2kw]

Floppa

[@karlmarx828]

Fanter

[@twentytwo_22]

What a beautiful list of candidates!

[@Sauspreme]

I bet that James has a relative note card in his pocket for every time he smiles and pauses

[@riccir75]

Is this only a decimal system problem? Because in hexadecimal you can solve 196 (C4) in two steps: c4 + 4c = 110; 110 + 011 = 121. And in binary system in one step: 11000100 + 00100011 = 11100111.

[@Donbros]

I love how he emds clip with pencil closing damn he is math showman

[@alexanderklein4118]

floppa femboy pcm

[@rgarciaf071]

I love the enthusiasm this guy has truly passionate about Mathematics

[@CrunchyFrog09]

No lie, I genuinely love numberphile, but the best thing about this video is the thumbnail

[@foppr8666]

This guy just makes me smile

[@jamirimaj6880]

One of the things I noticed about maths is that it's really hard to prove something when it concerns the digits of a certain number.

[@5gonza541]

3:58 Isn’t it odd that all their digits always add up to 16

[@danielyuan9862]

If you do the iteration once on all the given numbers (except 689) you will get the same number, meaning they are all correlated with each other.

[@theleftuprightatsoldierfield]

@@danielyuan9862they all end up at 887, which will get you to the same number as 689 after the next step