Numbery Card Trick - Numberphile

Uploaded by numberphile on 21.08.2012


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?
MATT PARKER: Yeah, if you leave.
If I-- oh, brilliant.
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.
And then if I fold this up.
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?
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.
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.

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.