I'm going to show you a mathematical
magic trick which is going to be incredible,
so if you'd like to take a card out-
(Brady: I can take any card can I?) - Any card you like.
I won't look at it but you can show the
camera. - (Brady: Okay, there we go.)
(What are you doing? You're putting it-)
I'm going to put it in the pack but
the idea is, using maths alone, I'm going
to shuffle your card to anywhere you
like in the pack. I'm going to do perfect
perfect mathematical shuffles, I'm going
to take it anywhere you like in the pack.
So you could say 43, and with five or less
shuffles I could take it to the 43rd
card, for example. So what what number
would you like? I'll write it down.
(Let's go for 22?) - 22, okay, if I write this down
here and then we won't forget it. I
reckon I could do that in four shuffles.
Each shuffle I'm going to know exactly
where it is with maths and then I'll
explain to you how it happened. - (What d'you mean by perfect shuffle?)
So exactly one after the other, so
basically...
See how it's one after the other? And I'm
going to myself three more and then it
should be at the 22nd card; so that's
three more shuffles. It's like threading
fifty-two needles at once, it's very
tense - that's a perfect shuffle. Two more
shuffles, two more perfect shuffles and
hopefully I'll have found your card
exactly in the 22nd place. That's a perfect
shuffle, that's good enough for me - one
after the other. I'll do one more and I'll lay them
out so you can see it's definitely
perfect. And just so you know they're
perfect; you can see it's exactly one
after the other,
so let's group them together.
Whoops a daisy- 22nd card are you ready?
(Brady: I'm ready, I'm ready and waiting) - Okay
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21 - what was your card? - (Ace of clubs.)
Ace of clubs - isn't that magical? By the
power of mathe-magics.
I'm going to explain it with - let's take
some of the hearts out - so; ok, I'm going
to put these on the top of the pack in
order 6, 5, 4, 3, 2, 1. Now, what I've done is,
just to demonstrate it a little bit I've
put the hearts on the top, the first
seven, just so you can kind of follow
what happens in a perfect shuffle.
So there's two ways I can perfectly shuffle
the cards like this, you might think
there's one way but there's two ways I
can do it. First way is going to look
like this, so this is the first way I've
done it and if I spread it out you'll
see - if I just look at the hearts what's
happened to them, the number of cards
above every card has doubled. So above
the seven that was originally six and
now there's 1 2 3 4 5 6 7 8 9 10 11 12.
Above the four there was originally three
and now there's 1 2 3 4 5 6, ok? So this
doubles the number of cards above every
card in the top half of the pack. If - I'm
going to write it here - if there was n
cards above it, after the shuffle there
was 2n cards above it. And because
this doesn't affect where the top card
was, it doesn't do anything, I'm just
going to call it a zero shuffle, that's
the name of that shuffle. Now that's,
that's say if I cut them- the pack in half
like this and I shuffled them like this.
So this top card stayed on top. The
second way I could shuffle them is I
could shuffle it like this, so the top
card would now be second from the top.
So it would look something - whoops - it would
look something like this, ok? So what this
does is it doesn't just double the number
of cards above every card, it doubles it
and adds one. So above the 5 there were
four cards, and now there's 1 2 3 4 5 6 7
8 9; it's doubled it and added one. Above
the four there was three cards, now there's 1
2 3 4 5 6 7. So what this shuffle does, if
there was n cards above it, afterwards
there's going to be two lots of n and an
extra one. And this now changes the
position of the top card, it does
something to it so I'm going to call it
a 1. Like it does something to to that
top card, it changes the place. Now we're
ready to explain to you how I got your
card to 22nd card. Basically, to begin
with you might have seen or maybe not
I'm not sure, that when I took your card
back I've secretly moved it to the top of
the pack. - (I didn't see you do that!)
I did, I secretly moved it to
the top of the pack. - (How did you do it?)
It was- well it's kind of like this, I put it in
and I pretended to show it to you like this,
there in the pack, and then I sprinkle
it but now it's there on top.
(I still don't see how you did that!) - Well that's
the bit you're gonna have to practice
maybe. So it's on the top of the pack. You
could you could do it any way you want,
you could even tell them to just put it
on the top. So maybe maybe you might have
thought it was in the middle, but
actually it was on the top of the pack. So
alli- when it's on the top of the pack
it's got no cards above it. If we want it
to end at the 22nd place - let me cover this
up - 22nd place it needs to have 21
cards above it. So all I've got to work
out is what sequence of doubling
shuffles and doubling add one shuffles
I need to do. So 21's an odd number so I must
have doubled something and added one. I
must have doubled 10 and added one, okay?
And that was a 1 shuffle, it was a
shuffle that doubled and added one. So
this is a number 1 here, not an arrow,
that's a 1. Ten's an even number, I must have
doubled 5 to get to 10 so that was
a doubling shuffle. That was a 0 shuffle
that took n to 2n. This is an odd number
again, so I must have doubled something
added one. I must have doubled 2 and
added 1. So that shuffle there is the
doubling add 1 shuffle, which we labelled
as at 1. That's an even number so before
having 2 cards above it I must have had
one card above it, and that must have been the
doubling shuffle. And then to get from 0 to 1
I must have doubled 0 and then added 1,
so that was a 1 shuffle. So where the 1
shuffle is the shuffle where I doubled the
number of cards above every card and
added 1, so this is double 0 add 1, a 0
shuffle is when I double the number of
cards above above every card. So here I had
one card above it and after that, after
that shuffle, it had 2 cards above it. And
then the 1 shuffle, I double the amount of cards above
every card and I added 1; a 0
shuffle I doubled the amount of cards
above every card and the 1 shuffle I
double the amount of cards above it and
added 1. When I say every card, I mean
every card in the top of the pack, top
half the pack which is where your card
is at the moment. - (Brady: Is that why you were)
(less fussy about the bottom half?) - Yeah, whereas the bottom part
didn't work out, it was okay cos I knew
your card started at the top and was just
working its way downwards, so the bottom
half didn't really matter. - (So you're)
(telling me, when you- you knew the ace of)
(clubs was at the top?) - Yeah
(So as soon as that was the case you knew you had to do a 1)
(shuffle, a 0 shuffle, a 1 shuffle, a 0)
(shuffle and a 1 shuffle?) - Yeah, well, there's
a there's a way to work it out. So this
is so this is 1 0 1 0 1, and actually
this is just a binary number. And if I
draw in what the values of each column
are, this is the number of 1s, this is
the number of 2s, this is 4s, 8s, 16s;
because that's how you count in binary.
So actually this is a 16, a 4, and a 1. This
is this is the number 21 in binary. So I
just have to work out what your number
is in binary, do that sequence of shuffles,
and it will take it to the right place.
[Extras] So if someone watching at home wants
to do this trick to their friends or
parents- - Yeah?
(There are- there's still a lot of barriers here, they have to)
(understand binary, which is maybe one of)
(the easier steps; they have to be)
(able to do perfect shuffles-) - That's true.
(And they have to be able to do the sleight)
(of hand to get the card up to the top.)
Yeah, well the binary; I mean sometimes I
don't trust myself to work out the
binary so have it written somewhere on a
piece of paper just in case. To get the-
to get the card to the top, you could do
loads of things; you have the ace of
clubs didn't you? I mean you could do- to
get the card to the top you could say,
they take out a card and you can say say
stop and they say stop somewhere and
they put it in here, but say you've remembered
what the bottom card is, if they say stop
there you put it in here you know once
you cut this in it's going to be
underneath that card. So it looks like
you've kind of mixed it in but you know it's
going to be underneath the two of spades
and you can go, I'm looking for the
card, looking for the card; I don't
know where it is. You could split it and
bring it there and then it's on top. So there's
lots of ways that don't take sleight of
hand to bring it the top. To do the
shuffling, if you want to do that way you
would have to practice it or you could
just take take them into halves and deal
them out one by one if you wanted to.
(That would make the trick quite slow.) - That would make the
trick quite slow; it's quite nice to
practice it and maybe maybe that's
something to aim for.