What I thought I'd show you a card trick that I like to call the Little Fibs trick.
So what we do is we take a deck of cards and we shuffle few times to make sure they're good and mixed up.
I usually do this with two people but we can just do it with one person.
You can actually do it with three or four people if you like.
And then what I do is, I have... I have a couple of people pick a couple of cards,
maybe I'll take off the top I don't know four or five that looks like five,
I mix them up thoroughly, and you tell me when to stop mixing.
- Brady: Okay, stop.
Okay, and then I have two people pick cards.
- Brady: Okay, so I'll represent both people here.
Okay, so pick... pick any cards you wish.
Okay. Now what you have to do is look at the cards and remember them.
Very important; suit and value. And then, the cards have values an Ace counts as 1,
2, 3 up to 10 is obvious, Jack, Queen and King is the usual convention of 11, 12, and 13.
So I want you to add the two values of the numbers, the cards that you have, but don't tell me that yet.
So if you got 3 and a King that would be 16, and if you got a Queen... two Queens that would be 24, and so on.
- Brady: So that one (King of hearts)
So remember the suit and the value.
- Brady: Suit and the value okay. (8 of clubs)
Okay. So now I have you put them back in the packet.
So put one back, maybe there and I'll cover them up... Cover it up. And put the other one back there.
And I'll cover it up.
Now a Magician would be able to find those cards and put them up very quickly,
It would probably already have it in his or her pocket, or perhaps in your pocket.
But I Mathemagician so I'm gonna do it little honestly. I'm gonna shuffle the cards again,
and make sure they're good and mixed up.
And ask you now what the two numbers added up to, the value total of the two cards you selected.
What was that please?
- Brady: They added up to... 21.
21, okay so it could be a Jack and a 10, it could be a Queen and a 9, that could have been two ten-and-a-halfs
there are many other possibilities ,and then there's the irrational numbers, we didn't even get to those...
I couldn't help noticing that you weren't wearing gloves
so in fact you left your fingerprints on the cards,
So I... I think from that point of view I might be able to find them.
let's see if I can do this now...
I'm looking for the fingerprints... I think I have it.
So let's shuffle them one more time to make sure that they're really lost.
And... And then I'm just gonna produce two cards,
and ask you what your cards were?
- Brady: They were the King of hearts and the 8 of clubs.
What, is it that king of hearts and that 8 of clubs?
- Brady: That was... That was those... it was them, you got it... you got it!
Good.
I'll shuffle those cards again, and we could do this again, but it's like telling a good joke.
The punchline isn't so funny the second time around. So you really don't want to perform this exact trick,
for the same audience, the second time.
But let me demonstrate what's actually going on here,
but this time I'm going to shuffle them in such a way that you can see a little more carefully what I'm really up to...
I'm indeed shuffling a lot of the cards, but if you look closely you'll see that I'm not shuffling,
quite a large chunk at the top.
so actually maybe eight or nine cards at the top, were not shuffled.
And I can do this several times and if I do it fast it looks like an honest shuffle,
especially if I don't give you the benefit of the angle.
That's the way I showed earlier. But if you see the angle,
and I do it slower you can see that in fact I have control over some of the cards, the top...
Five or six cards. Actually the top six cards it's what's particularly important.
So let me take them off, so I've done a false-shuffle here.
And giving the illusion of free choice. But actually, you're doomed to pick two cards from particular cards,
and I'm gonna show you what they are and see if you recognize them they're kind of famous numbers.
So 1, what might come after 1, well probably 2, what'd you think comes after 2 ?
- Brady: 3.
Most people would go for 3, what comes after 3 ? - Well, obviously 4. But wait a minute,
if I was to use these cards and you selected those two (2&3), you would tell me the total was 5.
But if somebody else selected these other two (1&4), they would also get a total of 5.
And that would be ambiguous. The whole point of this trick, is that from the total,
I do know what the cards are, even though I pretend I don't.
because you're picking from a controlled sub-set of the deck.
so we probably shouldn't use the 4, so in fact we might want to jump to 5.
Now we don't have the problem we had before.
Now what comes after 5 ? - Most people would say 6, but 6 isn't such a good idea,
because 6+1 is 7 and so is 5+2, so maybe we should jump to 7?
But 7+1 is 8 and so is 5+3. so we can't use 7, but it turns out that 8 works.
Now actually, we can push this a little further, we can go: 1, 2, 3, 5, 8, and another card.
If we do a 9; 9&1 is 10, so is 2&8.
Turns out we can't use 10, we can't use a Jack (11) or a Queen (11) either for similar reasons.
Guess what? - You have to go up to 13 which is a King.
At this point, you should be recognizing these numbers. They're very famous mathematics numbers,
for at least... 800 years; 1, 2, 3, 5, 8, 13...
Well the next one of course would be 21. These are the Fibonacci numbers.
And if you add 1&2 you get 3, if you add 2&3 you get 5, you add 5&3 you get 8, you add 5&8 you get 13,
you add 13&8 you get 21, it keeps going. But at that point, you're beyond the range of a deck of cards.
So for the cards, 'shark' - you only go with Ace (1) to 13 (King).
So I've chosen these particular Ace (1), 2, 3, 5, 8, and 13 (King), and I've memorized the suits.
I've been doing this trick for a while, so I put those at the top and I shuffle,
and you're gonna be picking cards from those too.
And it turns out that Fibonacci numbers have this magic property, that you will always
be able to decompose their sum.
So I pretend to shuffle, and I do in fact mix these cards up and I don't know which ones you're going to pick.
so again let me just show you two and you tell me what the total is,
and i'll tell you immediately what the cards are.
- Brady: 14.
14, so It's a King (13) and an Ace (1). Now, how did I know that?
I would say of course in performance well, it could have been a 7 and a 7, it could have been a 10 and a 4,
But I don't have 7's among the cards you're gonna pick from...
There's no other possibilities, when you have six numbers, there are - 6 times 5 over 2,
which I think is 15 different ways you can add them up in pairs.
Usually you'll get some collisions like 1+4 is the same as 2+3, but with these Fibonacci numbers,
you never get collisions - You'll get 15 distinct numbers.
and secondly, it's easy to actually break up the numbers. Here's the trick:
we'll try in again I'll just mix them up here and ask you to tell me what these two add up to?
what do those two add up to add up to?
- Brady: They add up to 15.
15, so here's what I'm doing in my head:
15 is the sum of two Fibonacci numbers. What's the biggest Fibonacci number - less than 15, I think it's 13.
So it's 13+... Well the subtraction's easy it's 13+2, so it's the King and the two.
And the suits, there's no mathematics involved there, I have to memorize the suits, but I do memorize the suits.
If you want to do this the first time, an easy version, just use the six values in question use all diamonds.
It's always going to be two diamonds, if you do the trick once for somebody, you'll probably get away with it.
It's a good way for students to learn to do the trick,
but for a more sophisticated version that's a bit more convincing use different suits and memorize them.
So I just again, happen to use the Ace of clubs, the 2 of hearts, the 3 of spades, the 5 of diamond.
Notice that suit order is C-H-S-D, called the "chaste order" and then you repeat the cycle of the suits.
So of course it's possible to get two of the same suit with six cards that's unavoidable.
I usually actually, leave the Ace out of the mix, simply because if the total's 3 it's too obvious.
A 3, could only be an Ace and a 2, and then the question of the suits isn't as impressive.
But if you leave the Ace out, it's quite impressive.
If you've been paying attention the beginning you might have noticed that I did in fact use the smallest
Fibonacci numbers 1 2 3 5 8 and 13 so that's the Little Fibs trick.
And to be honest I did tell a few little 'fibs' (Fabrications)
or if not, big whoppers because I said I was shuffling the cards.
"So what we do is we take a deck of cards and we shuffle... here we are shuffling the cards."
I couldn't possibly know what any of the cards are - those were little 'fibs', it was a fake shuffle.
I knew what cards you are selecting your two cards from, I didn't know what they were.
It wouldn't work with any five or six cards, you have to pick your numbers carefully.
And the Fibonacci numbers - work beautifully for this trick.
- Brady: so the little 'fib' was that you are serving me that little 'fibs'?
I was dishing up some little fibs.
What interested me, you can do other numbers,
for instance you can start with a 2 first and then a 1.
And then add those to get 3,
And add 1&3 to get 4, and add 3&4 to get 7, (The Lucas Numbers)