Beautiful Card Trick - Numberphile
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- Опубликовано: 25 ноя 2012
- Standup mathematician Matt Parker says this 27-card trick is the most mathematically beautiful - but it takes some explaining!
More links & stuff in full description below ↓↓↓
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"im gonna call the top pile the zeroth one, the middle pile the first one, and the bottom pile the 2nd one" this proves he's a programmer
He's working in base 3/mod 3.
loll yes!
"Famous brown paper'
+Maximillian Shirgene hahaha
This man is a legend XD
IKR
He has 5 stars in my book.
Max Max m
Any coincidence this is the 27th video in the playlist of Matt Parker's Numberphile videos?
+OrigamiPie Keima Katsuragi is my fav.~
Sounds like a parker square conspiracy.
yes
This looks like a good place for my favorite number-base joke:
Why do programmers get Halloween and Christmas confused?
Because Oct31 = Dec25
@s je except for the languages that don't use that syntax. Let's not forget it's just a joke
like
1+1 = 3
@s je that's actually just the syntax of some languages, not proper definitions. The '=' in how it's used in imperative languages does not make sense because you cannot reassign variables in math, so something like 'x = x+1' makes absolutely no sense from a mathematical or circuit standpoint. In some languages, '=' is the boolean operator and they have a symbol ':=' that means to set definitions.
@s je you sound fun at parties
s je
If you consider oct(x) and dec(x) as functions then I don’t see anything wrong with saying that oct(31)=dec(25).
And in the USA, they sometimes confuse those with Thanksgiving Day when it falls on Nov27.
The passion, you can see it in his eyes when he explains mathematics. This is a person who loves conversing with the universe.
Just wanted to point out (as was noted below by Sonja Quan) that this trick works equally as well with 64 cards. You have to convert the chosen number (number of cards from the top), minus 1, to base 4 using 1, 4, 16 instead of 1, 3, 9, and number the positions in the deck 0 to 3, top to bottom, and deal 4 piles each time (3 times), Otherwise it works the same way. This can be extended similarly to any deck of N-cubed different cards. Other generalizations are possible, if you don't mind dealing LOTS of cards.
Loved this trick! I've been dabbling in card tricks for awhile, but this was the first one I learned enough to actually try out on some friends. I added a few elements for the presentation. I split the deck in half (26 in both) then tell the spectator to have a card in mind and then pick either of the decks. I then tell them to go through the deck while I leave the room. If their card is in the half deck they have, they'll place it in the other deck and shuffle, otherwise they place any random card from their deck into the other deck. Either way, the other deck now has one more card and their card (27). Seems complicated writing it out, but it worked well. Then I come back in and perform the trick, doing some cuts while they tell me their favorite number. Probably the only simplification I might make is just tell them to find their card in either deck and then put a random card from the other deck in it, and shuffle. It worked really well and had great reactions.
i like this. also? a pack of cards is 52 plus 2 Jokers is 54 so ask the spectator to split a full deck and choose which 27?
When he said he was memorizing each pile's content every time. I was thinking, 'Wow, that seems like a simple card trick everyone can do."
Microcosmic Experience I was thinking how hard that would be
It's possible to do it blind folded! LIKE A BOSS!
brilliant idea!
wow.... best idea.!!! 👍👍
Yes it would
love this one, I show it to my students when I can. My Dad taught me this when I was a kid
“do you want to know how it works?”
“yes plea-“
“THIS, this is brilliant”
😂
those slow motion rewinds are hilarious
This trick is fun. I assisted my intuition by trying this with only A-9 for three suits and starting with them sorted. It's cool to see the symmetry, where you apparently shuffle the suits around the first couple deals and then end up with three piles of sorted suits in the last deal. Also, you can get a simplified version of this trick using four cards and doing a base 2 calculation. It's easy to get 1 of the 4 cards anywhere you want it in the pile with only 2 deals.
Great math! But it is also possible to use base 2 and 36 cards, base 3 and 27 cards, base 4 and 16 cards, base 5 and 25 cards, base 6 and 36 cards, base 7 and 49 cards (my favourite!). A great video by Matt! :)
I did this trick for friends and family this Christmas, was a success! My favourite part of the video is Matt's smirk at the end when he says "not many audiences will sit through the 10 billion version a second time", made me laugh.
There are two variations of this that I've used at work. One is to use a variation of the method from James' "Brown criterion" number selection video to get the person's number and then do the trick. The other is to use the first letter of the person's first name and use A=1, B=2 etc. to choose where the card goes, since 26 letters work well with 27 cards. When you're dealing off dummy cards at the end use letters instead of numbers, e.g. "A, B, C, D ... Q, R, S, T for Tony" and show the card.
Why don't you set up a shop where you can by the special brown paper?
thegamingmoose 10/10 would buy
+thegamingmoose You can buy craft paper at any office or art supply store.
+TexMex not the same
+thegamingmoose He used to sell it on ebay, haven't posted them in a while though
+Robert Balayan Gotta raise demand.
As soon as you said "27 cards" I knew the trick...considering it's the only card trick I've known for years and show it off all the time. Nice seeing it get some recognition.
always love watching and listening to Matt Parker's vids... makes them interesting
I've never liked magic or particularly card tricks but I loved this trick and have taught myself to do it. Best RUclips video ever thanks so much. Can't wait till Christmas.
That slowmotion...
I've thought of a variant. You have to be able to compute numbers in multiple bases though.
Ask the volunteer to pick any number between, say, 10 and 52, that isn't prime (call this number X). Then ask them to pick any divisor of X (call this number Y). Then ask them to pick their favorite number between 1 and X (call this number Z). Then do this trick with X cards sorted into Y piles each time, with the card ending up in position Z.
Stfu
Mr. Sheeb ...?
+Rabbit Cube That's genius! In practice, of course, your volunteer would need to know what prime numbers are and how to pick a divisor of their chosen composite number =)
So do we do this with the entire deck? And where in the pack do we put the initially chosen card ?
Say the number of card is A*B*C*D*... . In video A=B=C=3 but it works for any other values. You want to place the card at position N (starting at 0th).
Deal the cards first time in A piles.
You perform division N = A *Q0 + R0, set designated pile in position R0 in the deck, keep Q0 in mind.
Deal the cards a second time in B piles.
You perform division Q0 = B *Q1 + R1, set designated pile in position R1, keep Q1 in mind.
Continue this algorithm until you consume all factors.
A few summers ago, my cousins and I learned some card tricks and taught them to each other. I had learned this trick by watching this video. It's been so long now, I've forgotten how to do this trick, but watching this video again brought some great/fun memories
I learned a really cool card trick in math class. It's easy to do, no magic or math required. How it works? I have no idea but I know how to do it.
So take a deck of cards and have someone pick out 3 cards, make sure they remember so have them write it down or ask 3 people to pick one card each. Have them hold their 3 cards while you shuffle the deck. Then you're going to make 3 piles of cards. The first pile you put 10 cards down then to the right of that pile put 15 cards down then the third pile next to that will be 15 again. So you have 10-15-15 they are holding 3 cards and that leaves you with a pile of 9 cards, put those 9 cards off to the side. Try not to count out loud while making these piles. Just for easy reference 1st=10 left / 2nd = middle 15 / 3rd = right 15
Have them put down 1 of their cards on the 1st pile (10) then tell them to cut the 2nd pile (15) *ANYWAY* they want. They could take one card and put it on top of the 1st pile, they can take all but one card. Even or odd number of cards they cut it doesn't matter. Then have them put the second card on the 2nd pile ( the one they just cut) and tell them to cut the 3rd pile (15) again anyway they want and put it on top of 2nd pile. That leaves us with the 3rd pile where the third card will go, now take that extra 9 cards and put that on top the third pile so now all the cards are in 3 piles. Pick them up from right to left! 3rd pile on top of 2nd pile and those piles on top of 1st pile. Meaning the 3rd pile is on top 1st is on bottom. *Our deck is almost ready but this is important, take the first 4 cards off the top of the deck and put them on the bottom*
Now here's where the magic... or math happens. Tell them you're going to make two piles one pile face up and the other face down. Tell them to say stop if they see their card. So go through the whole deck starting with face up! So face up, face down, face up, face down. When you get through the first time you're going to take the pile of face up cards and put them off to the side. Now take the cards you put face down and do it again. Face up, face down, face up, face down all through the deck. Keep doing this over and over, you'll eventually be left with only 3 cards. Flip those 3 cards up and abracadabra you will have their 3 cards. And it will always be the cards they choose. However if you start with face down it won't work, forget to take 4 cards off the top before flipping it won't work or if you mix up the piles or a card gets out of place it won't work so keep the piles neat and tidy.
Hey man, I know it's been a long time, but can you give me a reply if you still use this account?
How much time did it take to write such a huge message?
1 hour,I guess...
Important to note: for this to work, TAKE OUT THE JOKERS FIRST
By doing this the 3 card positions in the deck are always in the positions (from top) 6,22,38. These are the only 3 positions where the method will work. This can also be done with the first pile having 14 cards instead of 10 so you dont have to take 4 cards from the top to the bottom.
My brain is now fried noodles.
Delicious
Famous brown paper :D
This was fascinating to watch, and did make sense. Thank you!
Imagine dealing a ten million card into 10 piles and that too 10 times and arranging them after each deal.
This is the only card trick that I could understand and successfully execute! Now it is time to show it off! XD
This is the only one I can't explain😅
Cqn u explain it to me
Who dislikes these videos? What were you expecting a channel called Numberfile to contain? A fetish for numbers with holes in them?
A number with holes in... sounds... *naught*y. I'll get my coat.
I disliked it because this is a very old and simple card trick. I understood how to do this and why it worked when I was 8 or 9. I expect something next level from this channel.
I dunno...those 6s and 9s...
Maybe they don't like his sideburns.
On the other hand... maybe they're just critiquing the video... I didn't find his explanation all that coherent.
My father first showed me this trick and I was so EXCITED to show it to my friends! ❤❤
Fabulous for my puzzle club, great intro into binary and working in different bases too. Thank you.
a trick using math.. Teachers at school should use this demonstration as an orientation to a new chapter or something
I don't think this takes a lot of math skill, if I am doing it correctly.
Whatever number they say, subtract 1. So let's say the number is 17.
How many times does 9 go into 16? 1 with 7 leftover
So with that 7 remainder we ask, how many times does 3 go into 7? 2 with 1 leftover
With that 1 remainder, we ask how many times does 1 go into 1? 1
So this gives us 1, 2, 1 In reverse order where 0 = top, 1 = middle, and 2 = bottom, we get middle, bottom, middle, and the card the person selected will be the 17th card in the deck.
+Christopher Draheim so basically, what you're doing is converting the number-1 into ternary, just like you're supposed to ^^ just in a different way than most would
but if they pick 27 27/9 = 3 so the universe implodes
Nah you have to subtract 1 from their number.
Knox you minus 1...
Yeah, I was thinking the same thing, seems pretty simple to me. I don't see why would someone need to be deep in math to do this. Exactly as you explained and as shown in this video.
one of the best non-music channels on yt .. love my math and science..i only knew 1 card trick and it happens to be a variation of this trick so now i know why it works
Shared this trick with my 8 year old brother and taught him about trinary with it. This is great!
i just adapted this to a Tarot deck using 64 of the 78 cards (4 stacks of 16). it impresses everyone who sees it.
You are wrong. The number of piles does not need to be equal to the number of steps (when you ask spectactor to tell in which pile the card is). In this case, we have 4 piles of cards and 3 steps. This give 4^3 = 64 cards. Each pile has 64/4 = 16 cards.
Tigrou7777 can this trick be done base 2?
Try eight piles of eight and use base 8. Then only two steps! 64 tarot cards required. Or add three extra cards to a full tarot deck for 81 cards and use base 9.
just like the standard deck comes short of 54, the tarot deck comes short of 81 lol
Makes me feel stupid, lack brain power to keep the sequence in my mind to do this trick =( Not the first time, at least
Amazing! This trick is really useful and wonderful. Thanks to Numberphile.
I love that you can do this trick with pretty much any number. As long it a multiplication of any other numbers it's is possible to do this one. My favourite is probably doing it with 25 cards, many are confused because I have to do the ordering only twice, whileas they kinda understand the 27 card trick. It's also fun to do it with 24 cards, but I haven't fully grasped that one yet, but it works ;)
Those smirks! Good stuff.
i wanna learn the trick at 0:04 ...
as a magician, I can only tell you where to learn it, go to 52kards riffle shuffle tutorial and he teaches the basics. just hold it in your hands.
It's not difficult, I learned as a kid. I also learned the one handed cut from Data on Star Trek
This is truly amazing.
Love this trick :) Thank you for sharing!!
When he spoke at 7:47 he should have said "when you give me your number I subtract one and then I work out that number in base three." If a given number is 7 the base three code for the trick to work is 020 or six not 021. right?
It took me a few watchings and a lot of deals before this clicked. I should have read the comments first.
Right
Correct
I understand completely but the video was a little long and hard to follow.
10:50 is all you need to understand, whatever number they choose (20), you take 1 away, (19) and work out how you can make 19 out of multiplication of 1, 3, and 9 using 0, 1, and 2. (0 = top 1 = middle 2 = bottom) You must mentally work it out and follow the order so that the 20th card from the top is their card.
20-1= 19
*1x1(middle) + 3x0(top) + 9x2(bottom)* = middle-top-bottom order to get 20th card from top as their card.
Thanks for the video its really amazing
This is a brilliant enhancement to the famous 21 card trick. I have always been intrigued as to why the 21 card trick worked. Your insight was very helpful.
could you please explain me 21 card trick mathematically ??
Go to walmart folks and go to the mail packing section and you can buy the brown paper in bulk
+TheAcenightcreeper I dont think anyone even cares
+jeffrey2014 I'm in England; no Walmart there is ASDA which is part of the Walmart family
pretty cool... BUT I was confused because he makes a mistake in his explanation....7:47 "when you give me your number I work it out in base 3"... actually, you would work out the person's number minus 1, in base 3... then it works.
He corrects himself by saying it's how many cards you want to put on top to make the card the n'th card
Just like there is no 10 in base 10, there is no 3 in base 3
This is a great trick! It also helped me really understand number systems other than base 10!
I love watching someone talk about maths and they actually passionate about it.. unlike my maths teacher. Good video :)
with that face at 0:00 , I thought you were gonna start chatting me up with numbers or something :|
my brain hurts...
I loved that video. I've known about the 21 card trick (and even worked it out once) but this one is much more elegant.
I have to admit, I was unable to solve a rubik's cube for years until I cheated and looked up a guide for the steps to move a particular square. I'm sure there is a mathematical reason for this (probably involving base 3) and would love to see a video about it.
I imagine it's much the same for people who solve rubik's cubes very quickly; they have memorized the steps, rather than understanding the process to solve it.
This guy is epic; saw him at the Maths inspiration event at Cambridge University.
Utterly amazing.
My favorite number is 17 because it is a prime number that is made up of the first 4 prime numbers added together (2 + 3 + 5 + 7)
Actually it used to be my house number before 911 changed it.
what do you mean 911 changed your house number??
Halberdier17 1+2+3+5 is 11
1 is not prime
doone By saying "911 changed the house number" means they had to move house because of an emergency. E.g. house on fire
doone 911 found it confusing because I lived in a neighborhood that didn't really have any street names. It was just the name of the neighborhood.
911 found that confusing so they changed everyone in that neighborhood's address by changing the house number and adding a street name.
Very cool trick. What if someone picked the number 27?
Bottom, bottom, bottom.
This is the best card trick ever!! I am going to try it whenever I have the chance, wow!
Thank you so much for that great trick !!!
pause at 11:55
Bless you.
Thanks Matt. Your video helped me get a gf
Matt is the real King of Hearts
@@foleyhuck2344 Now THAT was fantastic on so many levels! Well done, sir.
@@foleyhuck2344 Maybe the letter "f" and "h" at your name has switch places...
loved this
I presented this card trick to my class when I was 11 and I immediately became a permanent nerd. Thanks Numberphile 👍🏽
is it TheNumber27?
Yes
the dislikes were given by the people who are totally paralell with math
What a great video, dude!
You can also add the digits together and what group of three the sum is in determines the position, so 1 2 and 3 are the top 3, 4 5 and 6 are the middle 3, and 7 8 and 9 are the bottom 3. Then you find the final position by which group of nine the chosen number itself is in: 1-9, 10-18, or 19-27. For instance, if 25 the chosen number, 2+5 is 7, and 7 is the top number of the bottom 3, and 25 is in the bottom 9, so in the order is top bottom bottom
You can do this with 7 piles with 2 runs with 49 cards, just three off the top.
Nah I wanna make someone go “woah” not study math
I loved it! i tried to understand it some years ago, but i couldn't. Now I finally did it :') thank you very much :D
ahhh i love this!!! thanks a lot! :)
+Diogo Duarte If someone picked the number 27, you just always put the stack bottom.
bassisku Thanks! I realised that it was the number of cards you want on top of the chosen one and not the exact spot!
Put the speed at 0.5 at the start it seems like he is on drugs
+Sankeeth Persn (PurpleRox) Oh anybody at 0.5 sounds like they are extremely drunk.
BAHAHAHHAHAA
I CAN'T STOP LAUGHING ROFL
That's hilarious!
ikr
Great trick! I'll look forward to trying this with friends.
I was literally in awe for this was exactly the card trick we used to play when we were in elementary...can't even remember who taught us this trick lol..glad i stumbled upon it again for i totally forgot how to do it again haha
if i only had a deck of 256 cards
If only I had a deck of Graham cards.
I should have listened to my English teachers.
Dylan Addis Yea, well you can use personal cards with 1-64 and 4 colors.
this is very clever but the way I finish it is by making the 'victim' choose their own card from a big pile. there is a way to make them think they have have chosen randomly. you put all the cards down and ask them to choose a section. depending on which section they choose you either give it to them or take it away to make sure they end up with their card. everyone falls for it and it makes people realy baffled. this version is much harder
I know that way too
+Captain Rhodes i dont know a single person who ever fell for that.
Michael G. its all in the delivery. keep it fast and dynamic and it works all the time
Captain Rhodes no like seriously, thats like the most obvious trick ever. i know how to deliver a trick and sometimes even cover up major mistakes, but that? thats impossible, either for me or someone on the tv or whatever.
Got myself a deck of cards and tried that out. Only needed to watch the video like 3 times.
I am proud now. :3 And thanks for the trick!
Thank you for this! Never figured why the one with 21 cards worked, but really got the big ol' AHA! moment from this video. Cheers.
are you suppose to subtract 1 before doing the math because that's the only way i can make it work
Rubadubscrub substract 1 from what?
ie. yes is what the guy on top is saying
That's true or else you could throw x number of cards and show the x+1 the card
Wrng! I thnk mst ppl do
This trick is very amazing. I can't wait to show it off more.
I need to re-watch this when I'm not falling asleep
Can you do this with other bases?
+6XJOKERX I tried with base 2 but didn't have any luck :-/
+Mitch Etzkin It should work. If you try base 2, you should have a number of cards that are 2^n, split them into 2 piles, n number of times. How you order the two piles every time would be like in the video, but in binary instead.
+Victor Neo Okay let's assume that a player chooses a card (C) and puts it into the 3rd spot in the fan so that the list from top to bottom of deck is (LQCP). And let's say I want the Card "C" to be in the 4th spot at the end. 4-1 = 3 which in binary is 11, or in this trick every time I pick up the decks of cards, I put the deck that has my card in it on the bottom. So now we lay out the cards Imagining them being in piles with the top card in the column being on top of the pile and deal left to right:
CP So now my card is in first Column (Pile 1) so when I pick up my cards I put that in the bottom so the 4 cards picked up will be (PQCL). Now I lay them out again to get: CL
LQ PQ
Picking these up again will give us (LQCP), and card C is STILL in the 3rd spot, not the fourth spot. So when you did this it worked for you? Or I went wrong somewhere?
You can do it in base 2 with 16 cards.
2 piles and 4 repeats.
Same instructions
Mitch Etzkin you have LQCP, magic number is 4 and binary code is 11.
1)
Lay out LC, QP
Pick up with C at the bottom: QPLC
2)
Lay out QL, PC
Pick up, C at the bottom: QPLC
So C is the 4th card
I dont get it
+Chris Martinez Do you know how to count in ternary?
+Gadock the Kitten Also the numbers are 0, 1, and 2, because if you want to calculate different numbers you've got 1*x+3*x+9*x. Let's say number 9, meaning 8 on top --> 1x2+3x2+9x0=2+6+0=8
card is in the last 3, card is the last, card is the last in the first stack so 9th.
Last one, number 19, 18 on top --> 1x0+3x0+9x2=18, top, top, bottom. (card is in the first 3, card is the first, card is first in the last stack, so 19th).
think this video is better if u dont focus on the number and make a tutorial like any other magic channel
Chris Martinez don't*
Chris - I'm going to type two columns of numbers, normal (decimal) and ternary, side by side to show you how they progress:
dec ternary (or trinary)
0 0
1 1`
2 2
3 10
4 11
5 12
6 20
7 21
...
16 121 (= 1*9 + 2*3 + 1*1)
...
25 221
26 222
So, looking at the example above, 16 = 1*10 + 6* 1
and the trinary follows a similar pattern using powers of 3 instead of 10
I hope this explanation helps you understand the video more fully.
Hang in there, it's worth it.
This is actually a generalization of a trick I learned as a child. We always opted for the magic "7". Thanks!
We also played this card trick, but we didn't choose any particular number of cards like 27 in this case. We just selected some odd number of cards and same procedure was followed as you explained in this video with one exception. That is, every time we were keeping that pile of card in the middle of other two pile of cards. And finally at the end, guessed card exactly falls middle of the total number of cards.
What if someones favorite number is 1 or 2?
***** Isn't it top top middle for case of 2?
Howie Au No, it's middle, top, top.
+Mike Y This works either way since we can make "0" and "1" in Ternary (The way to start the trick is to take the "favorite" number and subtract one from it.) In Ternary "0" is 000 and "1" is 001, these two in deck order would be Top Top Top and Middle Top Top respectively.
Dude, I love how clever British people sound, reminds me of god damn doctor who.
This is one of my favorite card tricks to do because I'm not that great with sleight of hand or other 'magic trickery' that requires more physical skill, and there is no prep. Most of the other card tricks that use less skill involve some sort of deck setup/manipulation ahead of time. But the best thing about this is that you add that extra bit of aww and wonder to the spectator because you can let them shuffle the cards, then you can actually get a 2nd spectator to pick their favorite number, and at the end of the trick, neither spectator will have any idea how you do it.
It's different every time and even if someone watches you a few times and realizes you are picking the packs up in different orders each time, they still won't understand WHY that makes a difference,
It's beautiful.
THAT WAS SO AWESOME
Why is base 10 so special? we find it easy to think in base 10. Nature follows Fibonacci sequence and the golden ratio, both in base 10, why? You have just shown the magic of base 3 !. Thank you.
Because we are taught base 10 in every thing we do from the time we are able to understand math. Other base numbers are valid, but not easy to use for most people since they are not standard.
Unless from young they are taught numeracy through a different base, eg: 12.
the golden ratio and the fibonacci sequence would still be the same in any other base
Very nice trick. I tried different variations with different numeral system bases and amount of cards, and trick still works. Number of piles determines the numeral system base and number of times to choose pile with the right card determines cards required. So we can even make this trick making two piles, and asking to show the pile with the chosen card, say four times. Then we would need (number of piles)^(times to show pile)=2^4=16 cards.
I do this trick all the time... probably my second favorite, but I set it up in a slightly different way. Best thing is that it doesn't involve slight of hand, or setting the deck beforehand, or marked cards. Straight up math, but complicated enough that people are baffled when you do it.
I should start making homework... This is just so much more interesting :)
keep up the great work!
amazing trick! I'm going to show it to my friends and blow their minds haha
I love the excitement on his face!
Great trick - thanks! (5 years later) Tried this on two people - both impressed, but both said they knew it involved what order the card piles were picked up but couldn’t see a pattern. I would add one more twist (maybe it’s been offered in the comments already): Make a mental note of the remainder when you divide their number by 9 (if it’s 0 then make it 9 instead). This will be the “triplet” where their card appears when you lay them down the third time. Let’s say they choose 16 (so the remainder is 7). When you lay down the 7th triplet (i.e., the 19th, 20th, and 21st cards) on the third pass try to memorize those three. Then when they point to the pile it’s in you’ll know which of those was their card. Then as you count out the cards up to their chosen number just pause before turning it and ask “was it the 5 of hearts?” and then turn it over.
Dan Turney
If you show that you know what their card is at the end they might think you have memorized it and it would seem less magical
@jakob hill I think you may be right but I don't know why. The last time I tried this on someone I told them what their card was before turning it over and then revealing it seemed anticlimactic - it shouldn't though. I'm a lousy showman.
This comment, along with the graph at the end made it super easy for me to memorize how to do this trick, cheers!