21-card trick - Numberphile

A simple trick with some neat math behind it. More on Numberphile cards at: www.bradyharanblog.com/numberp...
More links & stuff in full description below ↓↓↓
More cards video: bit.ly/Cards_Shuffling
This video features Anastasia Chavez: anastasiachavez.academia.edu/cv
We did a similar video to this about six years ago with Matt Parker (and 27 cards): • Beautiful Card Trick -...
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/outr...
And support from Math For America - www.mathforamerica.org/
NUMBERPHILE
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[@numberphile]

More on Numberphile playing cards at: www.bradyharanblog.com/numberphile-playing-cards More cards video: bit.ly/Cards_Shuffling We did a similar video to this about six years ago with Matt Parker (and 27 cards): kzbin.info/www/bejne/omjPgWyvbKeVa8k

[@fingernailclipper2152]

Numberphile first like

[@RomanoPRODUCTION]

Numberphile, thank you for sorting the cards so nicely

[@luapnes]

I was gonna say, Matt Parker did this trick on your channel a while ago. Same principles.

[@Ronariverah]

Ahh Nostalgia, I was shown this tick as a kid in secondary school. I was just taught the sequence. I know there had to be math thing involved but never investigated further.

[@duckrutt]

Shouldn't one of the jokers be The White Gloves of Destiny?

[@daicon2k6]

Adding patter like "I'm a little bit nervous" is a nice touch, but adding Magician's Choice to the reveal is absolutely inspired. Brilliant!

[@machiningpaper]

Shouldn't the cards be sharpie on brown paper?

[@Triantalex]

??

[@MatthewSchellGaming]

I learned this card trick as a kid. Knew the idea of how it worked but nice to see it broken down.

[@KuraIthys]

Me too. It stuck with me. At some point I learnt how to adjust it to semi-arbitrary numbers of cards (I believe it still has to be a multiple of 3), but I've sort of forgotten the specifics of it. It's a weird trick, because it works even when the person doing it the trick doesn't know how or why. Really easy trick to pull off, since you don't need to do anything fancy, no sleight of hand, no fast movements, you don't even need a particularly clever story. As long as you remember the steps it just... Works...

[@dfess]

You can extend it to n groups of n^2 cards. The first step narrows you down to a group of n^2 cards, the second step to just n of those ones, and the last step singles out the one chosen card.

[@mdawsss18]

me too, but i've since forgot how to do it

[@jd9119]

If you learned this trick as a kid, you would've learned more than an idea of how it works.

[@Dylan-xv3hp]

Give the animator a pay rise for the dog shuffling haha

[@jondury9450]

Yeah, maybe even a pay raise.

[@kourii]

@@jondury9450 They say 'rise' in the UK and Australia (among others) whereas Americans say 'raise'

[@mohammadz1494]

4:15

[@Triantalex]

??

[@yaerius]

The first part, which is counting to know what card exactly was chosen is simple. It is the other part with removing groups that was impressive for me. It is also so simple, because you ask to pick, but you decide whether you remove the groups or leave them and remove the rest - brilliant in it's simplicity!

[@EmaDaCuz]

Showing off my skills with this trick since 1985. Now I am worthless. Thanks Numberphile.

[@AdelaeR]

Same here, only since 1989. Luckily though most people don't watch Numberphile.

[@ThePeterDislikeShow]

I've known this trick since circa 1992 A.D. Except I used the whole deck with stacks of 4!

[@lonestarr1490]

@@ThePeterDislikeShow Stacks of 4! ? That's 24 cards.

[@fudgesauce]

This is literally the only card trick I know. I probably learned it when I was 12 and I'm now in my mid 50s. In my experience, nobody is really too surprised you can figure out which card is their during the first (sorting) phase. But their mind is blown when they think they picked their own card, instead of you forcing it. No kids figure out that you are forcing their selection, but about half of all adults catch on.

[@danielyuan9862]

When my friend showed me this trick, I caught on to it, but I didn't point it out, because I didn't realize that it was part of the trick to make you think you had a choice.

[@vfacuu]

but can you make a Klein bottle out of a that card?

[@maniam5460]

Didn’t Matt do a very similar trick to this a few years back

[@MisterAppleEsq]

Yep. It's linked in the card at the top.

[@gaurishkatlana8730]

Yes

[@EddyProca]

He even disses this simpler version in that video.

[@gibbeldon]

That's why I immediately saw through this trick. :D You can even put the card at a different position than 11.

[@yuvalne]

The trick Matt did was the better version of this one. This one ensures the card ends in the middle, Matt's ensures it wherever you want it to be.

[@fuseteam]

after all these years i've rewatched all your card trick videos, i think. and now i understand how all of 'em works

[@somerandom3247]

This is the first card trick I ever learned (with a little different presentation), was cool to see the math behind it.

[@ClicketyClack]

This is one of the first tricks I learned when I was a kid. Still love it.

[@lowercaserho]

Those Numberphile cards are super sweet.

[@bsharpmajorscale]

They're no Parker Square, even if they feature one. ;)

[@RichardDominguezTheMagicIsReal]

I have been doing this effect for years with my own spin as a self working card trick, but now that I understand the math behind it I suddenly see a whole new world of possibilities to it

[@kacperk886]

This has been my go-to card trick since I was a kid. I've never thought about the math behind it but it makes sense.

[@luiss428]

i love the sound of the cards being set wtf

[@therealDannyVasquez]

What a lovely smile 😄

[@Triantalex]

thx..

[@thirumammalkanakarajano4956]

This is the first card trick that i learnt , and this inspired me to be a magician

[@jake0fc]

I've known this trick for a long time and ive been waiting for you guys and gals to do a video on it

[@HotelPapa100]

It takes a mathematician to explain this in modulo. Everyone else just sees the card to move towards the center.

[@manimax3]

Thats the only card trick I knew. Now everyone knows :D

[@stormsurge1]

Everybody already knew

[@jeffcolorado]

I'm a magician. Whenever I'm performing card tricks, there's always at least one person who says they know a trick. It's always this one.

[@manimax3]

+Jeff B they probably watched this video ^^

[@jeffcolorado]

Doubtful. I've been performing since the 70's, and had the trick presented MANY times back then, as well as now.

[@Triantalex]

false. :D

[@JustTakeAllGoodNames]

I learnt a version of this using 16 cards, back when I was year 4 (10years old) our teacher taught it to us during a maths lesson. I did the trick over the phone once to one of my friends, blew their mind!

[@sailcat9]

Excellent video. I would really like to see a video on the truly mindblowing NP vs. P problem and its profound implications. Thanks again and well done!

[@bestsnowboarderuknow]

The first trick I ever learned. Learned it from a Mexican in Cabo when I was like 11. it blows people's minds if you do it right. I've always wondered what the math is behind it, thanks for making this video!

[@deamon6681]

Only at the end when it was mentioned that the drawings are a special numberphile set I recognozed the faces. Well done.

[@AmodeusR]

You could also deal the cards in the end spelling "your card is" and after the "s" is their card.

[@TeamVacaville]

As a math teacher, with a degree in math, I always knew this trick had something to do with CoSets or something, but I am thrilled you explained this particular one. :)

[@SaruWaza]

The sound of the cards being shuffled and dealt is perfect ASMR material

[@RealRuler2112]

I must be the only one who hasn't heard/seen this one before... love it! Would very much like to see more like it. =)

[@JasperKloek]

it was new to me too.

[@hugopnabais]

My daughter was mind blown by this trick. Thank you

[@nymalous3428]

My brother used to do this trick in my church's youth group. He even taught it to a few of the other kids, and they were able to do it, but they couldn't understand why, which was interesting.

[@gavintillman1884]

Given that each location - left/centre/right - defines a ternary number 0/1/2 - and that there are three deals each yielding a ternary number - presumably the trick still works if, instead of dealing 21 cards, 3^3=27 are dealt.

[@calford2001]

Our computer science teacher made us code this a few weeks ago using Python, it is quite cool. It ended differently to this one but the start was the same

[@wonderpope]

I do a trick with 27 cards which uses this principle, but I can get the card to be in any position in the deck (in the video it lands right in the middle). In the beginning you ask to pick a card and to give a number from 1-27. by correctly putting the pile with the chosen card either on top, in the middle or on the bottom in the correct order after three times, the card will be at the chosen number in the pile. I'll leave the math to you :D

[@cristianavelar]

How??

[@beliasphyre3497]

People always tell me I'm not playing with a full deck. Glade I'm not the only one.

[@trod146]

Belias Phyre that's true since there is no e in glad

[@sabyasachinayak24]

I learnt this one as a kid and had fun figuring it out. You can also spell out Abracadabra, which has 11 letters, so that you don't have to remember anything. Just keep putting the selected column in the middle.

[@5quig]

I know this will probably get lost in the comments, but I really enjoy the videos on topology and physics. Could you make a video on the math/science behind a “Zing Ring” or a “Toroflux”?

[@ragnkja]

My cousin taught me this trick (without the last bit) when I was 10, and I figured out how it worked on my own, as well as that it would work for up to 27 cards.

[@naedolor]

you can do the same trick with 9 cards. It's the fifth. Learned these tricks 25 years ago. I'm still amazed how cool they are.

[@josephbokser2712]

I’ve been doing this trick ever since I was a kid. Great trick

[@zatarraagain7496]

Damn, that card design is awesome!

[@forestpepper3621]

To turn this in to a more general math question, we could ask, given M piles of cards, each containing N cards, what is the minimum number, S, of steps necessary to identify a selected card by this "stacking" technique? Will this stacking technique work for all possible values of M and N? Define the function S(M,N) in this way. So we know that S(3,7) = 3. Is there a way of computing S(M,N) in terms of standard operations on integers, such as taking remainders or rounding off fractions, etc ?

[@1smallstep]

It works better if you don't look at the faces of the cards; hold them up to the person, tell them to note which pile his card goes into, but never look at them yourself. This keeps a clever person from assuming that you remembered which cards were in column X, then remembered which cards remained in column X1, and so on.

[@christopherjuncker6672]

I was first showed this trick in the back of a moving 15 passenger van. and I am still not sure how all the cards stayed on the bench seat but I was one amazed kid after I was convinced I had picked my own card ad the end.

[@rickmorrow993]

My father showed me this one when I was a kid. He did not do the seven piles of three at the end, so that was a nice touch.

[@theCJoe]

I love this trick, learned it 18 years ago.

[@MrDazzlerdarren]

I used to do this trick when I was about 10; worked out you could get the card to any position in the deck depending on the order you stacked the cards over the 3 choices; top, top, top = 1st card bottom, bottom, bottom = 21st card and bottom, top, top would be 7th etc....

[@chascoppard]

Loved this trick as a kid

[@Craznar]

My dad showed me that trick around 50 years ago ... nostalgia central :)

[@pacman52280]

There is a book, written by Jon Racherbaumer, which shows a whole bunch of variations on this trick that take it to beyond the next level by including sleight of hand, so it longer is a self-working trick. It becomes a miracle.

[@lizardpeoplepoetry]

omg i remember this trick from when i was a kid! i hadn't thought about it in a long time.

[@nickrodriguez9935]

I tried different variations of this, different amount of cards, columns greater than 2 and rows greater than 1 and it worked every time but needed more time depending on the variation

[@RedRad1990]

Beginning of every card trick: *Magician:* "Just a bunch of cards" or "Please confirm this is an ordinary deck of cards" *Audience:* WHOOOAAAA

[@jamenneel342]

I saw a similar version of this in the book “Things to make and do in the fourth dimension” by Matt Parker, who often appears on this channel.

[@jamenneel342]

And there’s Matt Parker with a 27 card trick in the description... something to do with base-3, I would think.

[@laojackos]

The fact that James was the Jack was awesome, I hope he sees this!

[@ragnkja]

Katie Steckles and Hannah Fry are the Queens of Diamonds and Hearts, respectively, and I think the King of Hearts may be Tokeida.

[@laojackos]

Nillie this deck is the best

[@muhammadagilghifari2223]

The sound of the card was very satisfiying

[@robmoab3410]

Great vid as always! Can I make 1 request..... please bring back Simon for a video!

[@kushagrapiano9036]

Completely amazing

[@OlbaidFractalium]

When I was a kid I had a similar trick. Well, it was a very pretty animation.

[@Eburon]

I love Matt's card in the card deck

[@Bergarita]

I knew the 21 card trick and always knew it was the 11th card after the 3rd shuffle. The deal with the 7 piles of 3 cards at the end was a new twist. That is a manipulation in itself of the how the spectator "selects" the decks and how the magician manipulates the choices of what decks to leave on the table or take away. Then there is the final manipulation of the last deck left and which of the 3 cards to choose or take away finally leaving the original selected card.

[@KevinDay]

My favorite way to do this trick is to poke the 2 cards sandwiching their card out the bottom of the deck, ask them if it's one of the 2 visible, and when they say no, hit the bottom of the deck on the table and it pokes their card up out the top.

[@o_ber]

Dealing those cards was so satisfying.

[@EilrahCriS]

Take a sec to appreciate that shuffle sound

[@ehhorvath13]

I know how to do this trick! This is my favorite card trick to do as it is hard to decipher any pattern as the player.

[@apdgslfhsodbna]

it's awesome)) This is a power of Math )

[@SnowmansApartment]

The Numberphile cards are awesome XD

[@danne696]

When I was a kid, everyone knew this trick wasbased on keeping count of cards so I changed it up and memorized the first row picked and then just kept track of them so I could let anyone shuffle in between as much as they'd like. Was still stupidly simple, only reason people thought is was cool was because they assumed they'd know how I did it.

[@ChandrasegaranNarasimhan]

I figured out some parts of the trick. I could not get the removing card part. Interesting twist. Overall, smart, cunning and scary.

[@IndieMarkus]

So when performing this trick, you don't actually need to remember groups in between, but just have to remember that it has to be the eleventh card in the end, right? This makes it easier to perform the trick more convincingly if you don't have to count all the time.

[@cmck362]

Yeah if you always put the pile with their card in the middle then after the third deal it will be in the 11th spot.

[@JonathanCorwin]

You don't even need to remember it's the 11th. Just the middle card in the 4th group of three at the end.

[@IndieMarkus]

@Jonathan - that's not really easier in my opinion

[@rmsgrey]

If it helps, just remember that it's the middle card in the deck.

[@johnchessant3012]

Hmm... the "modulo 3" stuff would be more interesting with 27 cards, and you could express the positions in ternary.

[@AbiGail-ok7fc]

John Chessant The modulo stuff is a red herring and not at all required to perform, or even understand the trick.

[@kaesays1471]

There's another version of this trick that *does* use 27 cards and ternary by Matt Parker on this channel. Its linked in the description.

[@nayutaito9421]

Doesn't it work better with 27 cards?

[@akshaykumarsingh328]

Thanq u so much ma'am... actually u have taught math in a fun way👍👍👍

[@mattgsm]

My dad used to do this with me. its kinda fun. I then did 27 and used ternary to do a better version of it

[@diegosoltero4323]

So completely unrelated but I'm training for the Putnam and I was wondering if anyone knew a specific list of topics I should emphasize such or if there was any resources I could use to help me at least stand a chance

[@merrys6684]

idk how nobody asked this, but at the very end when you had them pick their card out of the last three, how did you make sure it was their card? i know it’s a one in three chance but still

[@KingSlimjeezy]

so this is what professors do during office hours

[@benfiner2450]

I learned this trick in school, but with 20 cards, using 4 columns of 5 and 5 piles of 4. I don't quite remember it, so I don't know how it worked because the math doesn't quite check out the way it does here, but it worked

[@jadnshay4life]

What if the spectator picks the pile (to be removed) with their card number?

[@TedTheTree]

I've know this trick about 40 years, you can change the ending to suit the effect if you like;

[@wingchunmac]

there is a similar trick with four rows where the flourish is making the card rise from the pack.

[@wdm2112]

I used to do this one when I was a kid!

[@jacksontcarroll]

card tricks and topological stuff and toys are fun and all but I really miss pure math stuff like Riemann Hypothesis videos... any way you guys can break down the Millenium problems you haven't covered (Yang-Mills and Mass Gap, Hodge Conjecture, Birch and Swinnerton-Dyer Conjecture, Navier-Stokes Equation) or something?

[@EVP5309]

This is the first card trick I ever learned, back in tenth grade.

[@hylens5111]

I love this one.

[@yukihirotaschchen3929]

if you just give the cards out and ask your friend in which pile his card is and repeat it three times, his card will always be in the 4th spot of a pile at the end. So ig you can make it easier for yourself

[@MarkWaner]

But the final part is tricky is not it? What if the person chooses card on the side? You still throw it away and continue with picking?

[@magicalpencil]

Was that a Hannah Fry card I doth see upon yonder table?

[@KittyBoom360]

I used to do this many years ago but with 4 columns (dealt by row then dealt by column) and fewer steps and no math.

[@WhiteboardMaths]

Now that is a cool party trick!

[@KuraIthys]

lol. You managed to add some extra complications to it I've never seen before. Interesting.

[@sinchevicieugeniu7414]

Watching this video from subscription feed if you know what I mean ) Great video by the way, will try it myself.

[@jbking6132]

I had a math question how do you take the derivative and intergal of a function with a factorial such as (x-1)!=y

[@pearltears8039]

When you ask to pick 4 piels what if they pick the pile with there faxed in it what do you do then?just ignore it or what?

[@Rygads]

I used to do this one in grade school! Baffled all my classmates!

[@ToniVarga]

How do you get remainders 1, 2 and 0?

[@sattikchakraborty5389]

can you please try to get the direct proof to steiner lehmus theorem ?

[@WillToWinvlog]

Wonderful!

[@olivier2553]

My grand dad taught me that trick when I was a kid, one day I decided I wanted to know why it works, it was not too hard to figure out.