got a pack of cards, I'll give you a quick look through them
you can see, they're kind of just in random order there
but this trick is about shuffling anyway
so we're gonna try to make them even more of a random order
and I'm not even gonna shuffle them, you're gonna shuffle them.
What I'm gonna ask you to do in a second
is deal out onto the table, as many as you like
let's try and make it roughly half, so between twenty and fourty
although it deosn't matter, and then you're gonna riffle shuffle the together
BRADY: Now this is me doing it for real everyone
JASON: There's your cards so you can deal
BRADY: Deal like this, like...
JASON: Yea, just deal that onto the table, as many as you like
BRADY: **counts mumbling**
twenty-two, tewnty-three, twenty-four, twenty-five, twenty-six, twenty-seven
JASON: so they sell it...
BRADY: tewnty-eight!  twenty-eight!
JASON: twenty-eight? okay, and I'll just order the up for you, so... ,  nice
and then you're gonna riffle shuffle those together
BRADY: hang on...
JASON: it's important to show you, Brady didn't do a perfect shuffle
even after all this practise youve been having and you've been telling me about.
So I'm gonna shuffle them in. Happy?
BRADY: Yep.
JASON: in they go
would't it be weird if, after the random number of cards you counted
after the riffle shuffle you did, you actually shuffeled them back into order
wouldn't that be strange?
ah, this is not quite where -
I mean you got two red, two balcks, I mean it doesn't...
look like you actually have, Brady, does it?
BRADY: No, they are not in order
JASON: mhh, not at all, except for unless...
unless I could maybe convince you, that actually, you did
shuffle them into order
'cos actuallly what you did, without realizing...
you shuffled it every two cards - every pair of cards, has one of each colour
the first two is a red and a black, the next two - red and a black
read and a black, every two cards...
has one of each colour, all the way through,
even if there's points , where there's a double red together, if we deal the off in twos...
strangely, each pair of two...
has one of each color, which, surely, you'd agree,
that's quite improbable
BRADY: Amazing!
JASON: But it get's much more
interesting than that because wouldn't it be
strange if every four cards had one of
each suit
there's a heart, a club, a spade, a diamond there.
the next
four cards
is a heart, club spade, diamond
even though they're in a different order
they're still definitely one of each
suit again a different order every four
cards to different order but it's
definitely one of a series four strains
and maybe you are better suffering then
he sought is quite impressive but you
know well Brady Joey done even better
than that
you shuffled its every 13 cars as one of
each value 123456789 10 11 12 13 have a
checkered restarting is definitely one
of each value NACE 23456789 10 Jack
Greene King's crazy 123456789 10 Jacques
Greene King one of each other again
isn't that strange again one of these
order and you'll notice it's weird
because the orders different in each set
of teen fantasy which he was allowed to
know some of the math behind there now
you can do to you can so that I K
rice I'm gonna show you the properties
of a permutation you go through when you
do that shuttle so the shuttle bay neat
deal out a certain number of cars and
then you whistle shuttle amend it
doesn't matter if it's not partly what
properties does that permutation have to
demonstrate it i've
numbered the cars just with the natural
counting numbers 1 to 2 52 and we're
gonna do that subtle to these cars to
see what happens asserting was you dealt
out some cars again it doesn't matter
how many Delta I think I think he did
you did you did a surprising what's
important here is when you deal and how
you were in the order was a crucial
saying so those are the ones at the top
now it's going to be the bottom 23456 28
says your turn to rate cards when you
order reversed now we're gonna riffle
least two together and the only thing we
can guarantee that this card is going to
get settled in above this card above
this card and so on its okay shes gonna
get riffle together in a second when we
put these together we're going to get a
new string of numbers day where we put
it together we're going to get a new
string of numbers and we're gonna look
at the crucial properties always occur
in this permutation so the first thing I
want to try and convince you is that
when we pushed together if we take the
first let's say 10 cards or 11 cause of
12 cause they will be a set of
consecutive numbers for example let's
say the first ones that I this first
again this time from this spot and this
one may be another 15 from this problem
maybe another one you can see what
happens whenever I add one to the bottom
of the policy shuttling together the one
I add is always going to be one smaller
than the small Escada house 001 bigger
than the biggest con how safe is here
I'm kind of counting down here and
counting now so I'm gonna be adding one
smaller than the smallest cause I have
641 bigger than the biggest card that
means that the cars I collect here we'll
all be consecutive just built and built
them up by taking one from one side or
the other side of this side the side so
obey consecutive string of No
others 36 27 28 29 30 so they are
consecutive even though the mixed up and
it didn't matter how many I take are
still get a string of consecutive
numbers even though that makes that day
as a guaranteed
and next thing I want to convince you of
is that the first K numbers will
different module ok to just in case we
don't know what modulo is modular is
essentially the remains you get when you
divide by the number so 605 is one that
has a remainder of 10 and 11 muslim
fighters also 125 is to go out to eat at
2525 and then we got the two alleged
look at will look at 54 now if you look
at the first five cards their
consecutive numbers and not in the right
order but these numbers are consecutive
we have five consecutive numbers is
actually a guaranteed that they'll be
all be different modulo 52 let me try to
explain that live there so I have
written out the first 16 counting
numbers and if I take the first five you
can see they're all different modulate
5/5 I get remained 2012 2-3 made it 4-0
and if I shifted up the next five
consecutive numbers of lost this July 15
game this one here they even have lost
his mother 1 I've gained this one city's
five consecutive numbers are still all
different level 85 and I could do it
again each time I shift up I lose this
modular five-game the equivalent value
at the top and you can keep on doing
that each time losing value but gaining
the equivalent modulo value at the top
so that means any five numbers will be
different if I actually any six numbers
will be different muslims 64 whatever
value we take and the sad fact that here
has taken out the first head of US
shuttle now we know that these numbers
are all different modulator if they're
all different modulo hair and then there
must be two of each value modulo five
can you see that here there's to
modulate 2721 Muslim 52 equipment to
2345 and so on so we got 10 numbers all
different on July 10 but two of each
module i-five says these five all
different module 05 and that means that
the next five also going to be different
Muslim thought and that if we continue
that on the next flight would be
different
slow fire and so on and so on continue
indefinitely
each SAT 05 has one of each value each
equivalent value modified that is all we
need to know about this trick because in
this trip we haven't actually use
numbers we've used as the values of
cards because these numbers starting
counselor they naturally cycle through
the different values each module a
separate set of 4 10 42301 mostly for
230 and so on
we can look at modulo 30 mins which
relate to the different values and so on
so to do this trick we need some of the
cars a cycle through the different
values just as the counting numbers
cycle through the different modalities
ok so maybe I can relate their clubs 21
months or maybe I can relate their
hearts to to mod for the spades
just three months for diamonds 2014 ok
so we know we're going to have a say
goes clubs hearts spades diamonds clubs
that space divers that also goes black
red light red light red so kind of
alternating modulo 2 as well and because
he wanted to do this thing with our use
of the cars the AC three kings we want a
system that cycles through the A three
kings and repeating cycle as well but
just having a 23456789 10 queen king
looks like it's an order parts or we do
we have us we have US tax system so it
looks mixed up but actually is a
repeating order to the very start when I
sobre the cars at first glance maybe a
look around them actually it was
completely or the completely set gonna
get them so they cycle through clouds
spades diamonds and also sell a cycle to
one of each value every searching cars
here is a pack of cars we got it
completely ordered
I'm going to use a very famous we're
stuck in the cards that uses a ride
eight kings threatened to save nine
ladies 416 knife I say why me
we're gonna go to website states that
eight kings the rat 310
say ladies 41 sick and we just do it
again but now we're starting the heart
we started reading the club now has
eight kings and to save nine ladies for
10 days he's sick I've got two more 816
see not only cycles just how the county
number of cycles
even so different values modulate to
this also cyber see black red black red
black grey black red just how the
counting numbers cycle through different
values modulate for space Diners Club
cards spades diamonds club hearts based
on his by the way the distance you to
use is chased see the club's 80 hearts
and then you can see just how the
counting numbers cycle three different
values modulate team we saw those two
different certain possible values of a
car's eight kings 310 2795 queen for a
six shot and then you can just start the
trek but I you can actually I just want
more convinced to do you can say is a
pack of cars all different cards and you
can let them give them a cuts you can
say to them I wanna I wanna let you
start the packet and ecology likes you
can cut the park anywhere any way you
like and then they can start from that
and I'll be fine because it was still
cycle through the different values in
order and the different suits in order
and read like where you can start with a
cut if you like
even more convincing this number further
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