today i have a card trick i'm going to
show you this card trick here we go
just a bunch of cards
and i need someone to pick a card so
let's
randomly pick a card out of there there
we go there's your card i haven't seen
it you're memorizing it and you can
stick it back in the pile here anywhere
i want anywhere you like okay all right
and just to be extra careful that i
didn't see anything
it's really
mixed up in there there's no way i could
know it i'm going to shuffle these cards
and then now i'm going to deal them out
into
three piles
and for show i need you to remember
this card so that you can mentally
pass along that information to me and we
can help that card
rise to the top okay so you point to
which column you see your card i see it
in this this one here okay perfect
all right so we're going to divide them
up again
and i hope you're remembering your card
because otherwise this trick might not
work
all right and now where do you see it
it's in this one here okay that makes me
a little nervous but that's all right
all right one more time just to be safe
okay something hard about this card and
where is it now it is
and this one this one oh
all right i think that's okay
all right
okay
so point two four piles for me please uh
let's go with
that these four here these four here
okay great
and now how about two piles from these
ones left uh
these two on the end the two on the end
okay
and one more
the one closest to you this one okay
oh no i'm feeling nervous
okay one of these cards please
um
middle one middle one
how did we do
did we do it
am i did i not make it
you got it i got it oh thank god
i was i was going to get a little
nervous are we going to have to do this
again
[Laughter]
that was
that was very good
right i imagine the people in the in the
audience are probably a little more
excited
maybe i'm a little more relieved
let's break it down so the first thing
we need to know is the name of this
trick is actually the 21 card trick so
the one piece of information i kept from
you is how many cards i have so i have
21 cards in my hand and so you can
really start thinking about this in
terms of modular arithmetic so i'm
thinking about
numbers and when i divide that number by
some fixed number like 3 i can ask for
which remainder does that number have it
can have remainder zero so maybe it's
like six divided by three has no
remainder seven has a remainder one so
seven divided by three i can get three
times two is six plus one so i can get
one and then i can also have two so like
eight divided by three has remainder two
okay so i can think about dividing up my
numbers any integer divided by three
into these three groups where the
remainder zero remainder one remainder
two okay so we picked and we picked a
card that was the first thing we did
should i do that yes please whatever
this time all right so here this time
two of clubs okay so everybody knows and
it's okay because eventually i already
was gonna know that but okay two of
clubs so we stick it back in and just
for show i i mixed them up this was this
is legitimate this was a real shuffle
yeah this is for sure i'm not doing
anything special here just to
to add to the enjoyment of the
randomness of it all i could have shot
you certainly
my my dog could have shuffled them i
guess
so two of clubs that's the one we were
looking for
the second step was to
divide them up into these columns so it
could have been anywhere at this point
the card can definitely be anywhere
but now i'm dividing them up into three
columns if you recall we discussed
modulo arithmetic so we're thinking
about dividing up 21 cards by three so
one of those cards has to be in the
column where you could think the
remainder is one the remainder is two or
the remainder is zero and so we see
our card here here it is okay okay so
the first thing we want to do is make
sure that this column has to be
sandwiched between
the two other columns and the reason i'm
going to do this is because this one has
seven cards in it i don't know which
card you know supposedly i don't know
which card it is
but i know now it's somewhere in
positions so there's seven here once i
put this one on top of these cards it's
got to be positions 8
9 10 11 12 13 or 14. so in positions 8
through 14 lies your card and then i'm
going to add the rest of these cards
here
and so that helps me know for sure it's
right in in this section 8 to 14. so
when i
separate them up again or divide them up
into these
three columns here are the first seven
those are the ones that i stacked on top
of my group no i'm not in there right
here comes eight so maybe i'll kind of
go like this so we can see 8
9 10
11
12 13 and 14. so there's that collection
of cards where your card has to live and
then i just
do the rest of them here
and what happened is i took 8 through 14
i divided it up by 3 and those numbers
have to have remainder one two or zero
and so it spread them across
my columns and now the rows that they
live in has shrunk so you can see
that whatever your whichever card we
know that we need to find has to be in
row
so this one goes in here just to make it
clear has to live in row three
four or five another way you can think
about it is as soon as i i do this the
same thing of
sticking whichever column you say your
card in which is here after seven cards
that means it's in position eight nine
ten eleven and possibly twelve because
this one had three rows involved okay so
now i'm looking at positions 10 11 and
12
that might contain your card so now i'm
going to pick up this column where your
card lives i'm going to put it between
the two columns of seven cards and now
we we're remembering positions 10 11 and
12. that's where your card should live
okay so here are the first seven
eight and nine here comes
10
11 and 12
and then the rest of the cards
so i knew your card should be somewhere
in positions 10 11 12 and once i've
divided those
cards up i've spread them across the
columns
and so now when you point to the column
i know exactly which card it is it's
this one
and now to to make it more exciting
instead of just saying oh here's your
card what i'm going to do is again take
a pile of 7
i'm going to stick it in front of the
pile that contains your card and then
the other seven afterwards
that means
one two three four five six seven
eight nine ten here's your card it will
always be in position eleven
so all i need to do
in this second the last part of the
trick is to count
so there's 3 4 5 6 7 8 9
10 11
12.
there's your card so as long as i've
counted and i remember where the 11th
card goes
now i can finish out my trick
and make sure that i remove all the
groups remove all the cards that are not
the 11th card and at the very end you'll
be amazed
you told me to pick groups that's right
what were you doing there at the end i
was making sure that whichever group you
picked or didn't pick it it never
removed the card that i wanted you to
find so if you said i said pick four
groups
and so you pick four maybe you pick
these four i take them away you don't
tell me before if you're going to keep
or get rid of what i choose not at all
because it's because you're picking it
so you told me that you first saw this
trick as a result of learning it like
with your children that's right did you
look at it and straight away think
mathematics or did you like how long did
it take till you started thinking this
is this is mathematical no i'd say
immediately i mean it didn't help that
the person who showed me the trick is
also a mathematician and we were with a
group of mathematicians so
it's already embedded in my brain that
there's math involved but i know that
there are 21 cards i see three piles and
there are seven cards in every pile and
you're doing it three times
i knew immediately math was involved
you're a youngster who doesn't
does she appreciate the mathematics or
has she just memorized i have to know
you know this is she's just learned the
routine she she loves the response yeah
she she knows there's math but she's
much more excited to get the people to
to shout oh my goodness when when she
pulls their card out she's just running
the algorithm oh for sure she's she's a
star she's a superstar she wants to be
uh on tv that's her that's her goal we
should have got here
i think so i i almost actually almost
kept one home today from school just in
case
i know what you're thinking you're
thinking gee i could really do with some
number file playing cards well if that's
the case check out the link in the video
description
[Music]