So dice tricks; again, this is from Martin
Gardner's book.
This is an absolute classic I think;
three dice, d6s, and I've got my little
blindfold because I'm going to pretend
I can't see - I actually can't see. Now I
could cheat, I could look through this
thing,
but I'm not right; and the point I'm
going to show you is that I don't need
to cheat, there's a way through.
So I'm going to ask you to roll the dice,
I'm going to blindfold myself from now on.
Can you grab those three d6s and roll
them for me- so
I'm going to ask you to do some adding
up, I know that's pressure but- - (Brady: Okay I can)
(do that. I can do that. Okay,)
(I've rolled them.) - Can you add up the
three numbers you can see - keep this
total running in your head; obviously I
can't see them. Now
choose one of the dice and check
the number on the bottom - show the camera -
and add that on.
That make sense? Okay can you re-roll
that one?
And add the one, on top of that one, that
you just re-rolled onto your total as well.
And now if you want to, leave the
totals pointing up, but like
put the dice together so I can't tell
which one got re-rolled or anything;
the point is that I can't
see anything about which dice you re-rolled
and I missed the re-rolling business. - (Yep.)
All done? I'm gonna take my blindfold
off now, but I've missed the crucial
stages.
And you're thinking of a number in your
head there's no way I can know that the
number is 16. - [Shocked gasp]
Except I do, because it's amazing. - (Wow,)
(that's pretty cool.) - I'm impressed that
you're impressed.
Let's try it again, I mean like like all
magic tricks, as we will say,
if you want to know how a trick works you try
and repeat the trick. I'm just going to
cover my eyes this time,
are you happy to re-roll again? - (Yep.)
You can be thinking about how it's possible
for me to know this and I'll show my
answer.
(All right, here we go. Okay.)
(Add them up?) - Yep, get it right,
pick a dice -
you don't have to pick the same one as
you picked last time. And check the
number on the bottom and add that onto
your total.
(Yep.) - And re-roll that one;
and then group them so I can't really
tell which one got re-rolled, there's no
way I can see it and I'm going to look
at these now.
So you have a number in your head? - (Yep.)
And that number
is definitely 12. - (Yep.)
Good. I mean the audience can't see
Brady's brain
whirring, like hmm- - (It somehow involves the)
(number seven?)
Go on- wait - good conjecture!
I need a bell to ring - conjecture - is the
number seven involved? Why do you say
seven? I know that some people will be
shouting that a bit. - (Because opposite)
(sides of a dice add up to seven.) - Does it help?
(Well the fact you made me turn one of)
(them the other way around makes me think)
(it must.)
Let's use your conjecture - we're kind of
working backwards here, like, check these
three dice again.
(There is a difference of seven there.)
Between what? - (Between the number)
(you said and what they add up to.) - Do you
remember what happened the first time?
(No.) - Should we do it again?
(Oh yeh alright, yeah all right, one more.)
I'm going to watch this time. - (All right,)
(here we go, here we go.)
(So that adds up to 12.) - I agree.
(If I take this one and add two)
(that comes to fourteen.)
Yeah and then you re-roll. - (17.)
And at this point I take my blindfold
off and I've missed all the crucial- - (Ooh)
(look and that's ten, so you add seven!)
(You add seven!) - If I tell you your
conjecture is correct,
now you need to tell me why.
And like all magic tricks when you spot
this, I guarantee you'd be like ah
seriously why did I not see that a
million miles off.
(Oh let's let's- all right let's let's let's-)
(Okay, so there we go, that adds up to ten.)
I agree.
(Adds up to ten. That's unchanged.)
(Add three, takes it to thirteen,)
(plus six - nineteen.)
And I can see- just that. - (Twelve- and that)
(twelve add seven gets you)
(up to nineteen. What-)
(what happened? I don't know what happened!)
It's- like all magic tricks, again it's
misdirection right?
You're at the heart of the problem,
you've got the key but the the way the
trick is presented
directs your attention away from the
crucial thing. I will make this really
obvious to you now I think;
when I take my blindfold off this is all
I can see. So what have I missed?
I've missed this one having its first
roll - what was it I can't remember?
Yeah, it doesn't actually matter does it?
Because whatever it was
you add the bottom number to it.
(So the first roll was irrelevant?)
Well it's not irrelevant. What matters is
the dice are set up in the way that you
know dice are set up - and this is the key -
opposite numbers of a die, d6, add to seven.
But that means the first roll
is that and that, and that's always seven.
It was always going to be whatever the
sum of those two is
plus seven plus that. You can't see the
seven anymore-
No, I know it's seven. - (Yeah, that's seven's gone.)
In the pub when you're
doing this, when we're allowed back in
pubs, so you do that, you glance and you
look away and then
basically you're panicking about trying
to add seven to the number you've just
seen on the table.
It can be done, it sounds difficult I
know, genuinely it's difficult under
pressure,
but all you've got to do is add seven to
that because you know that the roll and
the bottom -
before the re-roll - is gonna be seven.
That's it, like it's just seven.
But the obfuscation, technical word for
the misdirection,
is is neat enough; and a lot of people
know a lot of dice tricks that use the
property of the seven but this is one of
the neatest ones because it's right
there in front of you, if you break it down,
but the way the re-roll and the
performer claiming they didn't see the
re-roll
is the misdirection that you need to
make the seven
obvious. But it doesn't need a lot of
practice to learn and
you can adjust it, you can do it with
with four dice you just gotta adjust
what you expect to happen. You could ask
them to re-roll two of them; hey
the world's your oyster, and the nice
thing about magic in maths is that once
you've got the maths taped
you've got the sort of creativity of the
performance of the magic and the
misdirection and the story
to be creative about. So my advice is to
do it with
four dice, do it with different dice -
although there's a problem with this one,
octahedral dice? Five on that side, on the
opposite side
has a six, that's to eleven. One on that
side, opposite side is a two, that adds to
three.
This die does not have a consistent sum
on opposite faces,
and I don't know why. They could have
made it so it
so it did, but for whatever reason the
factory producing these is not doing it
when they are doing with the
the other die. And I was checking some
other dice, they seem to do it
for the dodecahedron dice, that does seem
to have a consistent sum,
and the icosahedron, but not the
octahedron.
And we could find a tetrahedron as well
but then we have a problem;
that doesn't have opposite sides. So my advice is
don't use that one; you can get away
with those if you
figure out what the opposite sum is, it's
not hard, but watch out for octahedral
dice - they seem to be made in two
versions and this version is one that
won't work for our little trick.
There you go, that's the three dice trick.
..This one- like it feels like it's rigged
against you,
I did it right and that's the luck of a
dice roll, that's why games with
randomness are interesting. - ..be the
second state.
Okay, this flap is below what he's
holding.
Now you cannot go from the first state
to the second state, because he's in the
way. - If it
wasn't true there would be only finitely
many exceptions.
Did we do it? Am I- did I not make it?
You got it. I got it? Oh thank God.