Hello, everybody!
Today, we're going to do a mathematical card trick.
So, first of all,
get your volunteer
to shuffle a pack of cards.
Then,
get your volunteer
to deal themselves
three piles of three cards each.
Now you're going to ask them to pick
one of the piles.
Get them to pick it up, and look at the bottom card.
Meanwhile, you collect the remaining cards.
and then get them to put their pile
on top.
Now, in a minute,
you're going to ask them
what their chosen card was,
but
you're going to give them the chance to lie.
So they could name any card that they want to,
and the pack is going to act
as a lie detector.
So let's say they name
the ace of clubs.
What you're going to do
is you're going to spell out
'ace of clubs.'
So first of all, you spell out 'ace.'
So it would be A-C-E.
Put the pack on top.
Now you spell out 'of'--O-F.
Put the pack on top.
And finally, you spell out the suit--so, clubs.
C-L-U-B-S.
Put the pack on top.
Now we're going to find out
if they were telling the truth
by spelling 'truth.'
So it would be T-R-U-T-H.
And the final card
was their chosen card,
and this will always work,
no matter what card
your volunteer decides to name.
They have a complete free choice,
but no matter what card they decide to name,
this will always work.
Let's see what's going on.
The blue card here is their chosen card.
The blue card now starts
in the third position.
So first of all, you start off by spelling out
a value--so let's say 'ace.'
So it would be A-C-E,
and put the pack on top,
and the blue card is now in the seventh position.
But if your volunteer decides to name something else,
so if they name a three,
if you spell out something longer,
like 'three'--T-H-R-E-E,
and put the pack on top,
the blue card is still in the seventh position.
Next, you spell out 'of'--O-F,
put the pack on top,
and the blue card is now in the fifth position.
Finally, you spell out a suit,
so if you spell out 'clubs,'
it would be C-L-U-B-S,
put the pack on top,
and the blue card
is in the fifth position, again.
But if you spell out something longer,
like 'diamonds,'
if you spell out 'diamonds,'
and put the pack on top,
the blue card will still be in the fifth position.
So their chosen card, the blue card,
is completely predictable.
You always know
where it is.
And you can finish off the trick
by spelling off 'truth,'
and that's how you end.
Now, what's happening to the other cards?
Is the blue card the only predictable card?
Well, here are the nine cards.
Now, if we start the trick again,
the top card
becomes the bottom card.
The second card
becomes the eighth card,
the third card becomes the seventh card.
Now, if you're spelling out a three-letter word
like 'ace' or 'six,'
the rest of the shuffle looks like this.
If you're spelling out something else,
something different like a four-letter word,
like 'jack,'
then that would look like this.
But if you're spelling out a five-letter word,
like 'three,' then the shuffle would look different again.
It would look like this.
But the only three cards we know for sure
the only predictable cards,
are the first three cards.
So let's just concentrate
on the first three cards.
Now, the second shuffle is always the same.
It's spelling out 'of'--O-F.
So the second shuffle always looks like this.
And then finally, the third shuffle
is naming the suit.
We can predict the first five cards of that--
that's always going to be the same.
So the first five cards
will look like this.
Putting it all together,
it looks like this,
and if you look at the third card,
the third card becomes the seventh card,
the seventh card becomes the fifth card,
and then the fifth card
becomes the fifth card again.
Now this is the only complete path from left to right,
which means that the third card
is the only predictable card.
And the other cards
really depend
on what your volunteer
chooses to name.
So it's a pretty good trick.
It's good fun.
And, as usual,
if you have been,
thanks for watching.