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Number Guessing Magic Trick · Acedra
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Number Guessing Magic Trick
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0:00
All right, Brady, I've got a magic trick for you. I want you to think of any number between one and 100. Just think of it in your head. All right, picture in your head. Try and transmit it to me. Yeah. >> Yep. Doing it. >> Yeah. Do something weird with your neck, Brady. What's that? >> I'm [laughter] pushing I'm pushing it towards you. I'm pushing the number out of my brain into your brain. >> Okay. I thought you turn into some sort of I don't know, [laughter]
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some sort of reptile or something. But Okay. Right now, what I want you to do is I want you to take I want you to look at this list. There's a lot of numbers written down on here. Yeah. I want you to think your figure your number again. I want you to tick every row that appears in. >> Okay. You're going to have to hold the camera. >> Oh, bloody hell. This is Oh my god. This is expensive piece of cake. How do I know I'm pointing in the right direction? >> Every one of my one's in. >> Yeah.
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>> Okay. >> I'll make sure you um don't miss any. >> Okay. >> Why is it ruin it and and try to transmit it to me? Your arms in the way. [laughter] >> I can't. >> Uh >> but you point Don't point to it. >> No, I'm not. No. Okay. Yeah. I've got to impress people with this. >> I think I think I've got them all. >> Oh, super far. You take that back. >> Okay. >> Okay. Now, keep keep transmitting that thought to me. [laughter] Right. >> Yeah. >> Let [snorts] me think about it.
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I think it's got a seven in it and a two in it. Is it 72? >> Yes. >> Yeah. There you go. Really? [laughter] >> All right. There we go. >> So, you impressed? >> What do you mean? Look how many numbers there are there. >> Yeah. Okay. Yeah. >> You should be impressed. >> Yeah. >> All right. Let me tell you the maths. Maybe you'll be impressed by the maths of it. Okay. >> Okay. >> Right. Okay. Now, let's have a look at the numbers. Now, if you look at these numbers in this little this little thing.
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>> Yeah. >> Right. The first number in each row, every single one of them is Fibonacci. 1 2 3 5 8 13 21 34 55 and 89. Do you remember the Fibonacci numbers? >> I don't know. Yeah. >> Yeah. So that's that sequence where you go one and then you keep adding to the uh the two before. So if you want to get generate the Fibonacci sequence, you what? You take fn which is the nth you add it to fn plus one and that will give you fn plus two. Right? So for example I mean you've done videos about this. You
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don't need to go through this again. >> Yeah. One one two three five eight. >> Exactly. So these first numbers are all Fibonacci numbers. One is Fibonacci. Two. Two is Fibonacci. Three. This is the Fibonacci sequence, right? And all I did was to get that answer. That's 70. Was it 72? I took the first one in each row. So, one of these numbers >> and added them together and it gave you your answer and it always works, >> right? >> Okay. But why is it working?
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>> So, show me show me what my four were. It was one >> one. Yeah. Three. So, that's four. >> Uh 13. So, that's that's now given us 17 and then 55 always works. This is something called base Fibonacci. There's something called the Zeonf decomposition. So, what do I mean? So, let's have a look at any number. It can be written in terms of Fibonacci numbers. So let me give you take the number 27 for example. Okay. I can write the number 27 as 21 + 5 + 1. Right? I can certainly do that. Yeah.
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>> And these are all Fibonacci numbers. This isn't unique. There's other ways in which I could write 27 in terms of Fibonacci numbers. I could write 13 + 8 + 5 + 1. I could do 21 + 3 + 2 + 1. Right? There's there's lots of different ways I can do it. But there's something special about this first one. Now, this first one, what you'll notice is that none of the Fibonacci numbers that appear in it are adjacent to each other in the Fibonacci sequence. >> As in like consecutive.
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>> Yeah, exactly. So, if I look at this one, so this this decomposition I've written here, 13 and eight are next to each other in the Fibonacci sequence. And in this one, well, actually, you know, three and two, for example, are next to each other in the Fibonacci sequence. This decomposition, this this particular choice which is unique for 27 is called the Zechonorf decomposition. And it's a decomposition in terms of Fibonacci numbers in which there's no two adjacent ones.
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>> And can every number be made in that way as well? >> Yes. Yes, it can. And this gives rise to base Fibonacci. I can probably squeeze this in there. >> You've got I've got another piece of paper here. [music] >> Heard about all the usual bases, right? So you know b base base two which is binary base 10 which we're used to using all the different bases. But there's also something called bass Fibonacci which is based on this second decomposition. So let me just write down
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the the few other Fibonacci numbers. I'll go up to 21. You could carry on of course going that way. And if I want to write 27 how could I write it in base Fibonacci? Well I know it's got one. If I do the zeonorf decomposition it's got one of 21s. It hasn't got any of these. Hasn't got any of these eight. It's got one of five. It's got no threes. no twos and it has got a one. So this is how you would write 27 in base Fibonacci. >> Once you've used one of these numbers,
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you hack it off the total and see what >> exactly. And actually Brady, you've just touched upon something really really important about the zeonor decomposition and why it exists. To create it, you use something called a greedy algorithm. So what's what's so what do I mean by this? And this this can explain why you never get two adjacent ones. So so let's give an example, right? Let's imagine that there's a sweet shop, right? Me and you like sweets, Brady. You know, especially
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when our when our wives aren't watching, right? [laughter] So, right, we like sweets, right? Now, so this let's say there's 100 sweets in this sweet shop. Then I go in first, right? And I'm greedy. I'm going to buy as many sweets as I can, but it has to be a Fibonacci number. Go. There's 100 sweets. Going to buy as many as I can. I need to find the largest Fibonacci number. Okay, that's below 100. Okay, that is 89. Okay, so I go and I get 89 sweets. Right now, you follow me in.
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You're a bit annoyed because there's not as many left now. And you go in. There's 11 left now, right? And you go in, you buy as many as you can. And it's got to be a Fibonacci number. Greedy algorithm. So, how many can you get? You can get eight. Okay? And we could keep going like that. Now, there was no way we could have ever had an adjacent number of of um Fibonacci numbers. Why? Let's take an arbitrary amount, any number of sweets in there. I go in first. I buy as
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many as I can and it's a Fibonacci number. Let me call it FN plus one. Okay, I buy this many. Then you go in, okay? And there's less now, right? But you buy the biggest number you can, but let's say you get the adjacent Fibonacci number. Let's say you do that. Let's imagine that's possible. And you're going to get a 10, right? And together that means we've got this many, which is >> a Fibonacci number. >> Another Fibonacci number. But I took as many as I could possibly take, right?
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>> And if and if it was a Fibonacci number to start with, that's how many you would have taken. as how many would have been taken. So that proves that it's impossible. It's precisely this greedy algorithm proves it's impossible to get the to to pick up those adjacent numbers and that's really the basis for the Zeon decomposition and uh why you get these unique representations in terms of Fibonacci numbers for any number and this is the core of this magic trick as well.
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>> So how were these lists created next to each Fibonacci number for this to work? What's the problem? So every number is if if if it's got if it's if it's got an entry one in here, it will appear in that line is basically the idea. So let's look at let's look at 27, right? So so so so I would claim that I'm going to claim 27's going to appear in the one row. Yes, it does. It's going to appear it's not going to appear in the two row. It doesn't. Or the three row. No, it doesn't. It will
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appear in the five row, I'm claiming. And yes, it does. So you can see it's going to it's going to pick out the Zeon decomposition. This is exactly how it's working. It'll pick and it'll be in 20 >> 21 >> 21 row there as well which so it literally picks out each one and that's how it works. So it's a magic with the with the zeundle of decomposition. >> I just think the trick's not that magical. >> What do you mean? Of course. Well, it's [laughter] mathematical magic.
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>> It's not that magical if you have to carry around this list with you and and require that much work and information from me. It detracts from the trick. But I love the mathematics. >> Well, I I think you're too fussy about your presentation on your tricks, mate. >> Have you used this trick before? >> I think I did it on my daughters and they weren't impressed either. I don't know. I think it's good. I really hope so. I hope it's definitely not finite, but I don't know if it's
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infinite at the moment. What I do know is this this this next one of the sequences at least as big as uh 2015. At least as big as that. [laughter] It You're right. You're right, Rey. You're right. It's way bigger. It's actually waving it.
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