21-card trick - Numberphile
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- Опубліковано 25 сер 2024
- A simple trick with some neat math behind it. More on Numberphile cards at: www.bradyharanb...
More links & stuff in full description below ↓↓↓
More cards video: bit.ly/Cards_Sh...
This video features Anastasia Chavez: anastasiachavez...
We did a similar video to this about six years ago with Matt Parker (and 27 cards): • Beautiful Card Trick -...
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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): ua-cam.com/video/l7lP9y7Bb5g/v-deo.html
Numberphile first like
Numberphile, thank you for sorting the cards so nicely
I was gonna say, Matt Parker did this trick on your channel a while ago. Same principles.
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.
Shouldn't one of the jokers be The White Gloves of Destiny?
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!
I learned this card trick as a kid. Knew the idea of how it worked but nice to see it broken down.
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...
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.
me too, but i've since forgot how to do it
If you learned this trick as a kid, you would've learned more than an idea of how it works.
Shouldn't the cards be sharpie on brown paper?
??
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!
Give the animator a pay rise for the dog shuffling haha
Yeah, maybe even a pay raise.
@@jondury9450 They say 'rise' in the UK and Australia (among others) whereas Americans say 'raise'
4:15
??
Showing off my skills with this trick since 1985. Now I am worthless. Thanks Numberphile.
Same here, only since 1989. Luckily though most people don't watch Numberphile.
I've known this trick since circa 1992 A.D. Except I used the whole deck with stacks of 4!
@@ThePeterDislikeShow Stacks of 4! ? That's 24 cards.
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.
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.
but can you make a Klein bottle out of a that card?
Didn’t Matt do a very similar trick to this a few years back
Yep. It's linked in the card at the top.
Yes
He even disses this simpler version in that video.
That's why I immediately saw through this trick. :D
You can even put the card at a different position than 11.
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.
Those Numberphile cards are super sweet.
They're no Parker Square, even if they feature one. ;)
It takes a mathematician to explain this in modulo. Everyone else just sees the card to move towards the center.
i love the sound of the cards being set wtf
This is the first card trick that i learnt , and this inspired me to be a magician
Thats the only card trick I knew. Now everyone knows :D
Everybody already knew
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.
+Jeff B they probably watched this video ^^
Doubtful. I've been performing since the 70's, and had the trick presented MANY times back then, as well as now.
false. :D
The sound of the cards being shuffled and dealt is perfect ASMR material
What a lovely smile 😄
thx..
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
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. =)
it was new to me too.
This is one of the first tricks I learned when I was a kid. Still love it.
People always tell me I'm not playing with a full deck.
Glade I'm not the only one.
Belias Phyre that's true since there is no e in glad
My daughter was mind blown by this trick. Thank you
You could also deal the cards in the end spelling "your card is" and after the "s" is their card.
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!
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”?
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
How??
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.
This is the first card trick I ever learned (with a little different presentation), was cool to see the math behind it.
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.
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!
after all these years i've rewatched all your card trick videos, i think. and now i understand how all of 'em works
Why 21 cards and not 27? Same number of steps.
Mitchell Thomas I like 27 because it *seems* harder than 21, but 21 is a nicer number for a lot of people... blackjack, 777, drinking age, etc.
Would it work with 27, or does it have to be 3 times a number not divisible by 3?
ljfa It works with 21 or 27, because in either case the central 7 or 9 cards are restricted to the same 3 rows in round 2 (3, 4, or 5 in the 21 card version; 4, 5, or 6 in the 27 card version). It won't work with 24, because the target card could end up in the 3rd, 4th, 5th, or 6th row on the second deal.
Edit: actually it could work with 24, but you would have to do some extra mental tracking and/or math to know if it is the 12th or 13th card. (If you use 27 cards, it's the 14th)
ljfa You can do the trick with any number of cards, and any number of columns, as long as you have at least 2 columns. You just may have to deal it out more often. If you have N cards and c columns the number of times you have to deal out the cards is the smallest integer d such that c^d >= N. So in the video we have c = 3 and d = 3, hence we can use up to 27 cards. 28 would not work.
Bryan Shepard This trick does not require any math. You don't always have to put the picked pile in the middle. You could put it always at the top or bottom, in which case the target card will be the first or last card from the last time the card was picked. You can then easily place it in a predictable place when picking up the cards a final time.
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 ?
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.
Beginning of every card trick:
*Magician:* "Just a bunch of cards" or "Please confirm this is an ordinary deck of cards"
*Audience:* WHOOOAAAA
The fact that James was the Jack was awesome, I hope he sees this!
Katie Steckles and Hannah Fry are the Queens of Diamonds and Hearts, respectively, and I think the King of Hearts may be Tokeida.
Nillie this deck is the best
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. :)
Only at the end when it was mentioned that the drawings are a special numberphile set I recognozed the faces. Well done.
so this is what professors do during office hours
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.
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
Damn, that card design is awesome!
Dealing those cards was so satisfying.
I've know this trick about 40 years, you can change the ending to suit the effect if you like;
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.
I do this trick but with a twist - I make the card rise out of the deck.
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.
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.
You don't even need to remember it's the 11th. Just the middle card in the 4th group of three at the end.
@Jonathan - that's not really easier in my opinion
If it helps, just remember that it's the middle card in the deck.
I've known this trick for a long time and ive been waiting for you guys and gals to do a video on it
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.
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.
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.
Hmm... the "modulo 3" stuff would be more interesting with 27 cards, and you could express the positions in ternary.
John Chessant The modulo stuff is a red herring and not at all required to perform, or even understand the trick.
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.
Take a sec to appreciate that shuffle sound
I figured out some parts of the trick. I could not get the removing card part. Interesting twist. Overall, smart, cunning and scary.
My dad showed me that trick around 50 years ago ... nostalgia central :)
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
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.
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.
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.
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.
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....
The sound of the card was very satisfiying
I’ve been doing this trick ever since I was a kid. Great trick
This trick is much easier with 16 cards, and you make 4 piles of 4. Then you only need to reorder it once, by turning the 4x4 grid by 90 degrees before making them choose the second time.
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.
A fun variation on this trick:
Count down 7 cards in a pile, then the next 7 cards you're going to alternate between 1/3 down and 1/3 up from the previous pile, so they lock in as if you were doing a riffle shuffle (1/3 overlap in the middle), the next 7 are going on top in a normal pile. You now have a pile with 4 cards sticking out the bottom and 3 sticking out the top. Grab the pile and squeeze the sides so that the pile is slightly bent. Now press the side with the 4 cards down on the table so the 3 cards on the other side rise, turn the pile upside down and press the side with 3 cards down on the table, turn once more (there should be 2 cards sticking out the bottom) and press down while exclaiming: "Was this your card?"
Loved this trick as a kid
I love this trick, learned it 18 years ago.
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!
I love this one.
My dad used to do this trick for me 30+ years ago when I was a kid
Listening in the backgroun: "My dog can shuffle these, I guess." *shuffling sounds* "Woof!"
I love Matt's card in the card deck
Completely amazing
I've done this trick with 15 and 27 cards....always blew my kid's minds...
You can also do it with 49 cards, 7 piles, and only having to ask "which pile" twice.
or really any squared number with X piles with X cards you can limit it to twice.
I knew this trick with 27 cards. It works exactly the same : deal 3 times in 3 columns and the chosen card ends up exactly in the middle of the pack.
This is the trick my dad taught me when I was a kid. It's not a trick actually it's Math 😁
can u help me? I dont know what to do if participant of this card trick choice the pile with his card, im really into this question
The Numberphile cards are awesome XD
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
omg i remember this trick from when i was a kid! i hadn't thought about it in a long time.
I've invented the "(any square number) card trick". So you can do it with any square number of cards (9, 16, 25, 36). So it goes the same but you divide all cards in a square Matrix (3*3, 4*4, 5*5, 6*6)... The great part, or the upgrade is that you only have to ask for the column twice, since sorting the first indicated column again in the square will give you exactly a líne, and only one possible card for the second question.
Then, the revealing part can be done as magically as you want/can.
Hope its clear and someone can rise the bet next time anyone comes up with the oldie 21 card trick ;)
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
This is the first card trick I ever learned, back in tenth grade.
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.
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.
And there’s Matt Parker with a 27 card trick in the description... something to do with base-3, I would think.
Doesn't it work better with 27 cards?
Great vid as always! Can I make 1 request..... please bring back Simon for a video!
I used to do this one in grade school! Baffled all my classmates!
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
I learned this trick from my grandmother when I was a child
Ohh so you do the opposite of what they choose if they choose the card? So if they say "those 4 groups" but the card is in there, then you take away the remaining 3 instead
It's a classic "false choice".
Someone showed me this trick when I was a kid and I immediately thought why limit it to 21 cards. The trick will still work for 27 cards. And they said WHAT NO IT WONT! And then I blow their mind.
Thanq u so much ma'am... actually u have taught math in a fun way👍👍👍
Now that is a cool party trick!
2:55, what is this 4 of hearts of diamonds at the top/right?!
there is a similar trick with four rows where the flourish is making the card rise from the pack.
I do wonder why it's been traditionally passed down as a 21-card trick when it's so clearly capable of distinguishing 27 cards (a round half-deck with jokers).
can somebody explain the last part with the groups? i dont understand how you dont stop the other person from removing the group you know their card is in.
This magic trick is passed down from father to son in my family! I think I'm the first to understand why it works aha
I used to do this one when I was a kid!