Okay would you like to see a magic trick?
(Brady: Always) - Okay so these are a set of four
little sticks that I've got here, they've
got numbers on them. They're called the
mental logs and I'm gonna use them to do
a super-fast mental calculation which
I'm sure you'll enjoy very much. So
you're allowed to order these in
whatever order you want to. So...
(Brady: Let's swap the middle two and then the end two)
And this end? - (Brady: Both the ends)
Both end twos. Okay that one and that one, yep. So
they've got four faces on each one so
what you want to do? - (Brady: I want to turn the)
(first one one.) - Like that?
(Yeh. The second one the other way.) - Yep.
(And the other two I want to flip completely 180.)
Okay. Like that and
like that? So you've now created four
four digit numbers across the top. So
you've got 4959
across the top there and
then three other numbers as well. And I
would like you to add up those four
numbers. - (Brady: 4959- ooh I'm not gonna tell you this.)
Okay I'll stop you there.
Before you press equals I'm gonna
tell you the total is going to be
22486. - (Brady: Awh let's see about that-)
(Oh okay, yeah. It was.) - It's a magic trick! Yes so this
is, this is a nice little- it's actually a
really classic magic trick. It's a thing
you can buy in magic shops and it's a
hundred percent maths and it's just, it's
adorable. Once you figure out how this
works it's actually super easy to do and
the maths is really really satisfying the
way that it actually works. So I mean if,
if people want to try and figure out how
this works you can have a look at them,
you can look at the numbers on them.
They've all got different sets of
numbers on each side. The the numbers- it
doesn't really matter what they are but
there is a pattern to it so you might be
able to look at some of those and maybe
spot some of the patterns in there but I
will explain what it is that's going on
here. So on here these numbers have been
chosen very carefully. So the the third
number there is the one that I'm
interested in, and that's the one that I
use to work out the total of all the
others. So- in fact I can do this with
fewer than four, I can do it with two
rods instead. So if I pick these two rods
like this I would say the total there is
275. And the reason I know that is
because I'm taking this number and putting
a two at the start; taking this number
and then minus
2 from that one. If I had these three
rods together I would say the total is
2777 because I'm putting a 2 at the
start and I'm subtracting 2 from that
last number. And in fact if I take these
and change them so that they're all
facing different ways like that- - (Brady: So there we'll have...)
(2755?) - Yep.
So that'll be the total for those. And
you can do it with one. So the total
there would be 21, because I put a two at
the start and I subtract two from the
last digit. And the reason why this works
is - it's just lovely. So if you look at
the numbers on here, the numbers except
for that third one will always add up to
the same total. So here I've got four,
nine and five, total of 18. Again, here
I've got nine, four and five, here I've
got three, seven and eight - total of 18.
And again three, eight and seven. And the
same thing works on any one of these; so
there I've got eight, three and seven -
total 18. Seven, two and nine - total 18; and that
will always work. And what this means is
that if you have your four columns of
numbers and you're adding them all
together you get 18 in each of the three
columns, plus whatever that extra digit
is. So what I'm essentially adding up is
whatever the number in the third row is,
and we'll come back to that later, but I've got 18-
- (Brady: I'm gonna do this one Katie.) - Yep.
(So, so this one is: 22722?) - Yep
(Okay) - So, yeh, you'll get a 5 digit
number if you've got four columns. And so
what I've essentially got here is, I've
got 18 in the right-hand column and in
this column I've got 18 again but
because it's the tens column I've
effectively got 180. And in the next
column I've got 1,800 and in the next
column I've got 18 thousand. And if I add
all of those together - do some live
maths, live very very easy maths - I get
this. And this number is 20 thousand
minus two. So if I take this row, which is
the only row I haven't used yet, add 20
thousand and subtract two I'll get the
same as if I'd added up all of the
numbers. And in that case it's the same
as putting a two at the start and then
minusing two from the number at the
end. So it's really nice. And and this is why
it works with any number of columns as
well, because the exact same thing happens,
I put- you know I just don't have this here
so I'd have 1998 and the
same thing would work. And also there's
there's an extra hidden thing built into
these, which i think is quite nifty, which
is that if you put the rods in this
order I can tell you the total on the
back is 28632.
- (Brady: Flip 'em around) - So if I flip
those over you can see I've got my
8634 which gives me
28632.
But in fact this number here
is the same as this number here, and this
number here is the same as this number
here; so they've deliberately- because of
course all you need is for those three
to add up to eighteen, you've got a bit
of flexibility in there. They've
deliberately made it so that whatever
this number is it's the same as that one.
So if I want to do the back I just look
at this number read backwards. So there
22722.
I do always enjoy checking in
to see what brilliant.org's problem of
the week is. There's a basic, intermediate
and advanced - let's go for the basic one, eh?
It says here 'Rakesh's spam filter
predicts whether or not an email is spam.
It is accurate 98% of
the time and he knows that one percent
of the emails sent to him are spam' - only
1%? I dream of that. 'Which is
more likely to be true if he receives an
email that his filter predicts is spam?
The email is spam or the email is not
spam?' While you think about that I'd like
to thank Brilliant for sponsoring this video.
brilliant.org is a website full of
quizzes and puzzles and courses you can
go through to get a better understanding
of things like mathematics, physics,
computer science. They've got brilliant
stuff and by doing all these quizzes and
puzzles and sort of working your way
through it you really get a better
understanding of mathematics. Not just
memorising things or being told things
you have to know, but encouraging
critical thinking. Really getting an
understanding for things. Go and have a
look at the website and if you go to
brilliant.org/numberphile, that
link's also in the video description, you
can get 20% off Brilliant's Premium
Membership. And let's see if I'm ready
for these intermediate and advanced- oh
the intermediate one's got a snowman!