Numbery Card Trick – Numberphile


MATT PARKER: All right. I’m going to show you
a math card trick. It is a genuine math trick,
there’s no sleight of hand, there’s no YouTubery. It’s not a sneaky edit or
anything like that. Everything you see is
the whole trick. It’s nothing else. And also because it is a math
card trick, it will involve a lot of tedious counting. So this is how this
is going to work. I have a normal deck
of cards, there are all 52 cards in there. I’m going to look through. What I’m going to do is pick one
of the cards and memorize where it is in the deck. So I’m going to pick one of
these cards, and then what I’m going to do is count how many
cards are on top of it. And I’m going to remember both
the card I’m thinking of, and the number of cards above it. OK, got it, got it. OK, so I’ll remember. I’m remembering one card in this
deck, and I’m remembering where it is. What I’m going to do now is
I’m going to broadcast the number of card into
Brady’s mind. All right? So I’m thinking of a
number of cards. I’m going to send that
number into his mind. He’s going to tell me that
number that I’ve sent to him, and then we’re going to
count off that many. And the next one will be the
card I’m remembering. Skeptical people may say you’re
just going to change your mind to whatever the card
happens to be, so I’m going to write down. In fact, I will show– How can we do this? BRADY HARAN: [INAUDIBLE]. MATT PARKER: Yeah,
if you leave. If I– oh, brilliant. OK. If I take– OK, so we’re going to
kick Brady out. He’s going to leave the room. Just briefly. Over here, this is
my prediction. So I’m going to predict
this card here. OK, that one there. Cool. And then if I fold this up. BRADY HARAN: OK? MATT PARKER: Hang on a second. Hang on. OK, you can’t see that. Actually, I’ll put
it down there. OK, cool. Yep, yep, you’re good. You’re good. So, I wrote it down on
a piece of paper. I openly scrunched it
up with one hand and I put it down there. But everyone has seen the
card I’m thinking of. So now, when I send this number
into your mind, the number, I’m going to count off
that many cards, and bam, the next one will be the one
that I wrote down on that piece paper. And in case it goes wrong, I
reserve the right to do this up to twice. At that point, we’ll
just call it off. OK, so here we go. Here comes the number, Brady. What is it? BRADY HARAN: 12. MATT PARKER: 12. OK, so I’m going to take off 12
cards, the next one will be the one that I wrote down. Here we go, ready? 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12. OK, next card. Next card is the
King of Spades. I did not write down
the King of Spades. That is not the card
I wrote down. But I tell you what,
we’ll try again. We’ll try again. We’ll do one more time. So, ready? OK, ready? What’s the number? Here it comes. BRADY HARAN: 15. MATT PARKER: 15 this time. OK, here we go. 15, are you ready? Here we go. 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15. OK, here we go. Did I write down, did I write
down the 4 of Spades? I did not. I did not write down
the 4 of Spades. What I actually wrote down
was the 8 of Diamonds. And you might think that this
trick is a bit of a bust. You tried to guess the number
twice, you said 12 the first time, you said 15
the second time. It wasn’t at either of
those positions. It turns out giving you one
number in your mind would be slightly impressive, sending
you two numbers would be even better. If you changed your mind even
slightly on either of those numbers, the difference wouldn’t
have been three. You actually had to take three
cards off, and then it’s the next one. And again, if you hadn’t
said 12 and 15, we wouldn’t have got 3. Are you ready? 1, 2, 3. The next card is the
8 of Diamonds. And now I just look
smug for a while. That’s my trick where I send
numbers into someone’s brain. Yeah, OK. It’s always, to be fair, every
time you do the trick, you have to deal it out twice. You have to put it back together
each time, and it always ends up being
the difference between the two numbers. And obviously, this started
off in a very particular position, and it was a position
where, by dealing it out twice, it always ends
up at the difference. There i one slight tweak,
depending on if the second number the person says was
bigger or smaller than the first number, and so you have
to do something slightly different in that case. But if you get a pack of cards
and you have a bit of a play with it, you’ll be
able to work it out reasonably quickly. OK, if you’re still here,
I’ll explain most of how the trick works. And so what I did, when I looked
through the cards, I was looking for them. And to be honest, I wasn’t
counting or anything, I was just looking to see what
the top card was. And as we know, it was
the 8 of Diamonds. So you look through, see what
the top card is, that’s the card you write down. So now, when you start sending
numbers into someone’s brain, you’ve got to pay attention to
what happens to the top card. So Brady, the first number
he said was 12. And so when I start counting
12, the top card off is the chosen card. 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12. And when you count cards off
into a pile, you’re reversing their order. Because what was the top
card is now the bottom card of this pile. And a lot of maths magic tricks
use the fact that you reverse cards when you
deal them out. So when I put them back
together, the 8 of Diamonds will now become the 12th
card from the top. In fact, whatever number your
volunteer says first, it will end up being that card
from the top. And so now, Brady picked 15,
which was a bigger number. And so as I count to 15, first
of all I have to count up to 12 to get to 15. So 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, and as the 12th card comes off, that was our original
8 of Diamonds. Because we’ve just reversed
12 again. And then you count 13, 14, 15. And so in fact, I’ve got to put
three more cards on top to go from 12 to 15. I have to put the difference of
the two numbers on top to go from the first number to
get to the second number. And when I put them back
together now, all I have to do is take off those three. So I take off the difference. 1, 2, 3. And the next card is
our friend, the 8 of Diamonds again. And so no matter what two
numbers they say, as long as the first one’s smaller, the
first time you deal, it puts it into that position. The second time you deal, it
reverses it back to the original order, and then you
put the extra ones on top. Once you take those off,
it’s right there. If you’re still watching, then
you want to work out what happens when the second
number is smaller than the first number. So I’ll show you again. So we’ll pretend Brady did the
same thing, but he said 15 first, then 12 second. So there’s the 8 of Diamonds,
it’s still on top. So first of all, 15. OK, so 1. There’s the 8. 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15. I put it back on top. Now, the trouble is if the
second number’s smaller, you’re not going to get back
to the chosen card. You’re just not going
to get far enough. But what you will do is you’ll
take off, well, let’s say 12. 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12. And then obviously you’re going
to do the thing with oh, no, that’s not it. It didn’t work, boo hoo. The trick now is instead of
putting these back on top, put them underneath. Because now you’ve put it into
the 15th position, which is the first big number. You’ve then taken
away that 12. In fact, it’s still the
difference between the two numbers, with one slight,
subtle change. Instead of taking off that many
cards and then the next one, you take off that many
cards as the last one. I’ll show you. So in this case, I would say oh,
you picked 15 and 12, the difference is 3. Wow, it’s actually
the third card. Here we go, ready? 1, 2, 3. And there it is. It’s the third card. And so it’s still the
difference, but all you need to do is make sure, instead of
counting off all of them first and then revealing it, you count
them off and turn over the last one. OK. What if they pick the
same number twice? Now, if they pick the same
number twice, then what you need to do is– I mean obviously, you can play
off the fact that they’re very, very insistent that
that’s the number. And you say look, you seem
very insistent mean. In fact, you’re right. That is the number
I was sending. Something just went wrong
the first time, so I doubted myself. But you know what, it probably
is that number. Then you count them off again,
and the important thing is this time you count off that
many times, and then you turn over the last one
you’re counting. So I’ll show you very quickly. So 8 was the top. Let’s say Brady said
12 the first time. 1, 2, 3, 4, 5, 6, 7,
9, 9, 10, 11, 12. Oh no, I got it wrong. I’ll put them back on again. And then he’s like
no, no, I insist. It’s definitely 12. You go OK, well we’ll check. Maybe it’s just the 12th card. Maybe that’s the number I’m
trying to send you. 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12. Oh, it is. Wow, how about that? It still works. So there you are. That’s what you do if they say
the same number twice. JAMES CLEWETT: Here we go. Here’s my home made
lottery balls. I’m going to give them
a little shake. And I’m looking away because
I really don’t want to cheat here. Looking away. I’ve got one hand in there. I’m pulling out a ball,
and it’s number two. MATT PARKER: Yes, there
is one more option. What if they say 1 or 0 at
the very, very beginning? And if they say 1 or 0 at the
very, very beginning, this is perfect, right? And this has actually
happened to me. Twice now, someone said
1, it’s the top card. And so what you do is you go,
really, the top card? You really think
I just put it– And t hey go yeah, I’m
absolutely certain. You go, well good, I’m glad
you’re certain, because it is the top card. And then their brain blows up. It’s absolutely amazing. And I think that is
all the options.

Author Since: Mar 11, 2019

  1. its based on a 27 card counting system, there is no 52 to choose unless you broaden your trick size which alters all the fundamentals of this very trick

  2. I had a deck of cards and was doing this with him. I was shuffling the cards as he was explaining what to do if they pick 1 or 0, and i flipped over the top card at the exact same time as he did. It was the 8 of diamonds.

    My brain blew up.

  3. actually, if the second number is the same as the first, it's not a problem: you can say that the difference is zero, so there is no card on top of the one you put in the deck and ta-daaa it comes out that the first card of the deck is the right one. the problem is when the first number is the second plus one: in that case, the second time you reveal the n-th card, well… the card is really there! so prepare to say something like "the first time you were close, now you perceived it right!"

  4. When he said that we have to write down the top card, I immediately understood the trick. And it is so simple!!!

  5. there is a problem if they choose 3 and then 2….but I guess in this case I will tell them I sent a right number in their minds in the first place 😀

  6. Say, "Okay, well, go get me another deck to add to this one and we'll see if you're right." As long as you put that other deck on the bottom of yours, it'll still work 😀 .

  7. So. If a person say's 10 first, then 20 second, you will land on number 10 again, and the cards would have changed?

  8. I was shuffling a deck cards whilst watching this, and when I looked down at them, I realised that I'd accidentally turned over a card while I was shuffling them. It was the 8 of diamonds.

  9. This is a mechanic that can easily be added onto to involve audience members picking the card. Add a little sleight of hand into the equation and you can really make a brain-teasing trick that's guaranteed to baffle people. Not many magicians actually mix sleuth tricks with math tricks, but when it's done well, it's really good.

  10. If you try this with your friends, remember: If the first number is greater than the second number, for example 10 and 3, you have to do something slightly different.
    a) Put the second "number-pile" at the bottom of the deck – not on top. So the second pile, here 3 cards + 1 flip card, goes to the bottom.
    b) Then, count the difference from the top as usual. BUT, you must flip your magical card on the count of "7" (10-3), not the following 8th card! This is because the 3+1 cards has been put at the bottom of the deck.

  11. What if I think of 51? You would need to reverse the whole stack, whereas anyone would now say "just show me the last card" (51+1 = a deck of cards)

  12. Here's my slight variation on this trick:

    If N1 < N2, put the second "fail" card on the bottom before counting the difference.
    If N1 > N2, put the whole second pile underneath as Matt did.

    That way you can be consistent with how you count the cards (always turn over the Nth card, instead of counting N and then turning over the next card).

  13. When a person chooses a smaller number second (e.g., 7 followed by 5) you do not need to change the trick and present the 5 card. Simply ask them to choose the second number, in this case 5 and place the 8th card on top of the pile you just counted out instead of placing in back on the the main card pile. Proceed with placing the "counted" pile underneath the main pile and count out 2 in this example and the 3rd card will be the card you wrote down.

  14. What if they say 5 and 10 or any other pair that one is twice the other? Then the difference would be one that they already guessed and the reveal wouldn't work.

  15. But if they pick one less than the original on the second run, you just seem like a failure at your first attempt :/

  16. Nice. Covered all of the possibilities. I like the MIT  (Magician In Trouble), syndrome. This effect is a great follow up after an ACAAN (Any Card At Any Number), effect where the effect is carried one step further (if it ever comes up that the spectator is sceptic of the first effect ), by allowing the spectator to pick the number where the card should be in a sense that you sent the number to the spectator, yet leaving the spectator with the thought that the spectator really received the number that you sent or the spectator could have picked any number that popped in their head. This is perfect when the spectator is sceptic that the performer is really not sending the number to them mentally and the spectator just say any number to see if the trick will work. So, when the effect still works, in that case,  this makes the effect all the more powerful!

  17. I'm 6 years too late, but if you don't to change it to "oh, it's just the third card, not the card with three cards on top," you can flip the the "guess card" on the dealt pile on the first guess, then on the second guess if the number is smaller, don't include the card. That will put a buffer card in the deck before the target card and you can still do the reveal like normal. (If the second number is bigger, just do the same as the first time, adding a buffer card the second time around, evening out the math.) This also solves the "one fewer" problem.

    Also, if they say "1" that just means there's 1 card on top. If they say "0" then it's the top card.

    However, I'm realizing that the charade can fall apart if they pick a number of cards close to zero. If they say "1" then "0" the trick doesn't work. And if they say a very small number, they might catch that the cards just switched order and that's how it worked. Especially if they say "1." My solution: While "picking" a card, tell them you're not going to pick the first or last card so they don't think you cheated when you shuffled. It's the perfect con.

    I think I might switch this up so instead of "sending the number" I have them guess or something to make the difference between numbers seem more organic.

    Awesome trick! Thanks for the video!

  18. So if I'm seeing this correctly, the first choice is half of the second choice, then it's even better because the first trip through gives nothing then the big reveal gives the right card and it was the same amount as the first choice.

  19. Most useless video. There is no great mathematics in knowing that order of cards get reversed. This is a boring trick and definitely nothing interesting in terms of math.

  20. I always forget how YouTube comments didn't always have sub-threads for direct replies until I watch videos that are like 6, 7 years or older and see comments [usually from the uploader] that are seemingly nonsensical and talking to nobody, when in reality they are actually in response to another comment and replies just used to be their own comments

    Really makes me appreciate the current comment system, honestly.
    But remembering the old system reminded me of the spot above the comments where folks could "submit" [for lack of a better word] a video to be there as a related/response video [I don't remember specifically what the term was, if there's anyone who's as much of a fossil as I am who's actually understanding what I'm talking about, let me know] with the uploader's approval

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