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  • 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)

What I thought I'd show you a card trick that I like to call the Little Fibs trick.

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Little Fibs - Numberphile (Little Fibs - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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