I've been reading some Martin Gardner
books, all sorts of gems in there, here's
one I haven't practiced very much.
It just needs a die. I want you to pick a
number on the die, don't tell me what it is.
So I can't actually see anything at all
which means that you
can feel free to sort of, I don't know, show the
the video watchers-
(Brady: Let's go for that number.) - A whole number
right? You haven't got a picked pi or
something?
(No it's a- it's an integer.) - Okay
(And it's on a die.) - Good.
You should be able to see three numbers
on the die. (Yes I can)
Can you see your number? - (No)
Interesting.
Can you see your number now? - (Yes)
That's interesting.
Can you see your number now? - (Yes)
(Is it the one on top?) I think so.
(Yep, you got it.)
[Laughter]
Well I'm excited.
[Laughter]
(How did you do that? Can you can)
(you teach it so people can do it to)
(their parents?) - I can do.
Do you have any idea- because I've never
tried this trick on anyone before and,
first of all, with all magic tricks
there's a trick right? But when you know the trick
the thing's lame. I've just done a lame thing.
Is it at all interesting
that I could know with- blindfolded what
your number was?
(Yeah!) - Okay, can we try it one more time?
And I think you might
start to spot what's going on, like all
magic tricks you repeat it and you're
like wait a second. So
so you you decide a number
again. - (Let's go)
(for - uh - let's go for that number.) I'm
trying to point a corner towards you so-
it's interesting on a D6, you can only
ever see three numbers. Can you see
your number now? - (No)
Interesting. So let's try the question again there,
can you see your number now?
(Yes) - That's interesting, what about,
what about now? - (No)
That's very intriguing,
why would you choose that number?
(Yes!)
Why would you choose a 1? I mean that's
what lost you in that pig game
When I first saw this I was
like, ah it's like what they call a
binary search.
A binary search is where you're hunting
for something that you don't know and you
try and eliminate half the possibilities
in one go. And that's kind of the key to
this; I'm asking three questions.
And that should be enough information,
it's just that doing it with a blindfold
somehow makes it feel
surprising. I'm still surprised that I
get it right-
Audrey I know you're impressed too-
(Audrey!)
(Audrey - out!) - Do you want to roll a die?
- No? Okay. - (Out. How do we-)
(how do we do how do you do it?) - So a
binary search - get rid of half the
options with each question.
And a moment's thought reveals that
I've only got six options. So first of
all I could ask six questions;
the trick would be a bit rubbish - is it
1? No, is it 2?
I guarantee you- I think I did those in
three questions
and if you halve something three times
actually you've reduced from eight to
one; so
three halvings should be plenty of
questions to get this. So
that's the that's the base principle;
like I'm just asking enough questions. So
I think I can talk you through
this; the first thing is is one of the
six numbers I ask a question which is,
can you see your number? And if you say
yes what do I know? - (Narrowed it to three.)
Yeah and I'm blindfolded but I can still
feel there's three faces there there and
there that I know you can see. If you say
yes I know it's those three, if you say
no
I know it's one of those three. So I've
halved it. And then the next question is,
if I ask you then-
let's say you say no on that and I spin
it round, if I then ask you
can you see your number? It's a stupid
question right because I know you can,
so I need to hide one of these. And all I
did was spin that forward
and now I know that two of them are ones that
might be your number. And if I say can
you see your number and you say no,
I knew that these two were possibles and
the one on the bottom
is also possible. And you can't see it so
the one on the bottom
is your number. But if you said yes then
it's one of these two so I just need to
hide one of those two
and now that one's the only possible one
that you can see,
or it's the one that you can't see. So if
you say no it's that one,
if you say yes there's that one. - (Let's)
(use the number 1 again.) - Okay so you've
chosen 1 but I don't know that; I'm
blindfolded, I can't see anything. But I
know that if I spin the die
so that you can see three then I ask a
question, yes or no, can you see your number?
And in this case you would say yes, so I
know it's one of these three.
If you'd said no I would have known it's
one of those three. In this case it's not
so I've already got
half the solutions out of the way. I now
want to ask again;
if I didn't move it I wouldn't be
getting any new information so I'm going
to hide one of these three, gonna hide
that one. So now
I know that these two faces are
possibles and the one on the bottom.
So can you see your number? - (Yes..)
So I know, even though I'm blindfolded, that it's
one of these two, so let's hide one of
them.
Can you see your number? - (No)
It's the one I just hid which is on the bottom and
that's it. And because of this halving business
I'm guaranteed to get down to only one
left
in at most three turns. In fact it might
go even quicker.
(Let's do it now if the one wasn't visible)
(in the first go.) - Okay, and I'm also going
to rig it slightly to show how it could
go even quicker but-
can you see your number? - (No.)
So under the cover of my hands, if
I'm blindfolded I'd spin this all the
way around and that's my mental check,
right it's one of those three numbers;
and I would hide one of them. Now I don't
know which one to hide but I've just got
a sort of consistent way of rolling it
so I'm convinced I know where it is.
And now I say, can you see your number? - (No)
And I know it must be the one I've just
hidden then so which point I just clean up,
walk away, in two turns and that's
nicer. Although as a performer for me I'm
like
it just feels really lame, I've just like
just asked a couple of questions. But I
still think the effect is quite nice and
it's a nice demonstration of
searching efficiently. And it also means
that if eight is what
doubling three times gives you - so
halving three times gets you back to one -
I've got more than enough information, I
should be able to do this on a D8.
(Can you do it with the D8?) - Mathematics
says I can;
practice means I'm a bit nervous but we
can have a try. This is an octahedron and
it does have eight
sides- - (But I can see four at a time now!)
Yeah that's true, so we've got-
and I think if I aim a corner towards
you you can only see those four - can you
see those four?
Okay, the most difficult thing with
me in my blindfold is like orienting
the dice so you can actually see the
four, because if I put it like that I
don't know what you can see.
(Well do you want to do this one)
(unblindfolded?) - No we'll do it blindfolded
(All right, should I choose a number?)
Choose a number; don't tell me
whatever you do. - (All right,)
(let's go for that number.) - So you and the
camera can see
four numbers? Can you see your
number? - (No)
You can't see your number? So I'm kind of
hiding what I'm doing, you might want to
speculate about what I'm doing.
Let's go with-
can you see your number? - (Uh no I can't.)
You can't see your number?
This is the bit that I'm just super
feeling my way about.
Can you see-
Oh dear - can you see your number now?
(No!) - Interesting
Your number is on top. - (On top there?)
(Do you want the good news or the bad news?)
I want both.
(You got it!) - Yes!
But I knew I was going to get it all
along because I'm supremely confident in
mathematics
and my tactile blind handling of a D8.
(Let's do the five again.) - So you go for
five so can you see your number,
yes? But all I know is it's one of these
four. My next job is to halve the amount
of information so I need to hide two of
these faces; so I did that
in this case by just rolling over like
that. I know that two of the ones you
could see are now missing but two of them
are visible. So can you see your number?
(Yes) - So I know it's one of these two.
I'm kind of feeling with my first two
fingers each time thinking it's one of
those two. If you'd said no
I knew it'd be one of those two that I
first showed you, but I've got to keep
track of where they are with my blindfold.
But since he said yes I know it's one of
these two, so I just got to hide one of
those two.
So let's just roll it onto there, so I know that
one of them is on the bottom, that helps
me know where it is, and one of them is
visible and I know it's the front one. I
say can you see your number and you say
no, in which case I know it's the one I
just hid so I flip it over
and flourish or something. And sort of
start sweating about whether I've
actually got it. - (Nice!)
But it's it's a nice example of like
searching efficiently if you've got
a lot of things, trying to halve it each
time is one of the most efficient; and
that's partly why
binary as a number system is like used
in computers because it's kind of an
efficient way of thinking about breaking
up numbers. And that's just a nice
demonstration of
a binary search. The fact that you can do
it on a D6 - Martin Gardner talked about
doing on a D6 and I was like,
that means it must be possible on a D8.
(Can you do a higher D now?) - There's
some options right? There's a D10 - that
could be done in
four questions. D12,
the dodecahedron icosahedron, that could
be done in four; and that could be done
in five. But it's hard, I mean I'm finding
the octahedron hard enough.
So I'd need a lot more practice but it
could be done and the thing is I start
to doubt whether the impressiveness- like
four questions
feels like quite a lot. The fact that the
D6
sometimes works out in two is what gives
that little kicker like boom boom, got it.
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...Well of course we
know what it means in practice, we mean
if we throw it,
you know, it should land on each of the
30 faces a 30th of the time. But
let me talk about that for a second. When
I was a graduate student
we had a guy who was a retired executive
who wanted to test the laws of chance-
And well this means more often than
that that's the end of the story. So the
totem pole continues like this,
this one beats this one and this one
beat this one.
So I think- this is almost for the simple
game you're not playing against someone else,
aim for 20 is a good piece of advice.