Beautiful Card Trick - Numberphile

MATT: Okay, I'm going to do a

card

trick

based on the number 27. It's my favorite

trick

. I will demonstrate it today and explain it at the same time. I found it in a 1950 mathematics book written by Martin Gardner. For me it is the

card

trick with the most

beautiful

mathematics of all. And since it is a mathematical trick, we have to count a lot. But keep it up. I need 27 cards, so I take 27. Just counting. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 27 is one of my favorite numbers... 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. .. because it is a third power. 1, 2, 3, 4, 5, 6, 7. Well, that's 27 cards. It works with any 27-card set and you don't need to be skilled to use it.

And it's not the magic of YouTube either, where I edit intelligently. I'll explain it to you later. It goes like this: take 27 cards and mix them well. I use Brady as a videographer and volunteer. I slide them and you touch what card do you want? Well, this one here. Do you want to show the card to the camera? Of course not for me. Return it somewhere? Thank you. You just have to remember which card it was. If you're wrong, I'll read it in the comments. Brady, what is your favorite number between 1 and 27? Just pick 1. BRADY: 10. MATT: 10, for any special reason?

BRADY: It just looks good. MATT: Do you agree with that? OK. Are you looking for your card now? You have to look carefully at which pile your card ends up in. Some have seen this trick before. It is a variation of the 21 card trick. What pile is it in? BRADY: In that pile. MATT: In the middle? Okay, I'll pick them up, for the viewer from right to left. What people usually do is count endlessly all the time. But I just memorize all the cards from the beginning. So when you said what pile it was, there were only 9 possible cards left.

I'll do it again. Due to the way of distribution I reduce the number of possible cards to 3. What pile is it? BRADY: Now it's in the middle. MATT: Back to the middle. Okay, pure coincidence. I pick them up again. Once again to divide by 3 again because 27 is 3 to the power of 3. If you say what a bunch, I know what card it is because I have memorized all the cards from the beginning. That's all for this trick. What battery is it? BRADY: This one? MATT: That one over there. Great, okay. To be honest, I wasn't completely honest.

The numbers are correct, the number of cards went from 27 to 9, to 3, to 1. That is absolutely true. But I didn't bother to remember them. I actually did something completely different. What was your card? You can tell me now. BRADY: He was king of hearts. MATT: King of Hearts. What was your favorite number? BRADY: 10. MATT: Okay. See this. Here we go. Finalized? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. King of hearts. The trick is that you can put the card anywhere, without knowing what it is, anywhere in the deck. If you give me a number, I can get the card at that location by splitting it three times.

That's my favorite math card trick. Do you want to know how it works? BRADY: Yes, please. MATT: It's brilliant. Well, can I have some of your famous brown paper? Okay great. Now let's see why the trick works. Pay close attention to what I do. I look at cards in a special way. With 27 cards, the last step of the trick (we look from back to front) is to collect them into three piles of 9 cards. From now on I will call the top one zero stack, then the first one, and then the second one. There's a reason for this, which I'll tell you when I'm done with this.

So when they come back, there are 9 cards in the top pile: 1, 2, 3, 4, 5, 6, 7, 8, nine. That's why I called the top stack zero stack. There are also 1, 2, 3, 4, 5, 6, 7, 8, nine in the first pile. And the bottom one, 1, 2, 3, 4, 5, 6, 7, 8, nine, that was the second pile. Your card was the king of hearts. And that had to be the tenth letter. Since you already said that was your favorite number, 10, I had to go there. If you think about it, the top three of the bottom pile... because they're the bottom of the top, middle and bottom stack... The top one came from the previous top stack.

That was the previous zero stack, that was the middle stack and that was the bottom one. That was the previous top, middle and bottom. Up, middle, down. So if you look closely you can see what's going on. I picked them up after the second time. I have the top, middle and bottom stack. Each of the 9 cards I put back together. I split 3 piles again and the first ones come from the top pile of 9. The next 3 too, and finally the next 3. Therefore, the top 3 come from the previous zero heap. The following come from the middle pile. So 3 in the middle, 3 in the middle and 3 in the middle.

We have 0 left, which come from the bottom pile. So now I get 3 from the bottom, 3 from the bottom and 3 from the bottom. So they will be positioned like this. If you take some cards and play with them a little, the last time you pick them up from the beginning it turns out that they are top, middle, bottom. Up, middle, down. Up, middle, down. Don't think too much about why this is the case. Grab a deck of cards and do it. You will see it automatically. This order is there from the first time you share. I'm sharing this for the second time, and this is the order from the last time we shared.

Then get to 10, which is this position here. Or top, top, middle. So when Brady pointed to the pile, I put it on top first, then on top again, and in the middle the last time. The first time I put the battery on top. The second time I put the pile on top. The last time in the middle. Brady, would you like to choose another number? BRADY: If I said my favorite number was 13, what would you do? MATT: OK 13, I need 12 cards on top of that, 12 is a 9, a 3 and a zero. So it will be top, middle, middle. 13 is nine, 10, 11, 12, 13.

See? 0, up, middle, middle. Actually, I solve it with number base 3. The whole trick uses number base 3. Ternary arithmetic, not seen often. It's really amazing. The first time the units are number base 3. Then the column of 3. And finally the column of 9. So if you give me your number, I will convert it to base 3 number and then I will know how to put the batteries back. Okay, we'll do the first trick again. I almost did it in slow motion. You chose a card and then I started sharing them. Then I started talking about your favorite number, you said 10.

You were looking for the king of hearts and I thought how do I get that king of hearts? Haha, I don't know what card he is. How do I get any card in tenth position? 10 contains 1 times 9. So I want 9 cards on top. So it will be top, top, middle. Have you seen King of Hearts yet? Where was he? BRADY: He was there. MATT: Well top, top, middle. If I pick them up from left to right these two don't matter. They can be medium or lower. The king of hearts is on the top. Then he gets to the first nine cards on the table.

It will be the top, the middle, whatever, or the third of the following piles. The rest doesn't matter at all. Because you knew from those piles that he wasn't in them. They are simply filling in to get the right positions. Which one was he in now? The one in the middle? OK, he was top, top, middle. So this bunch has to rise again. If you watch while I pick them up, you'll see that I do it in the same order. But putting it in my hand is different. So one goes up, that one goes down and that one goes down.

Now I know he's up there. Even among the top three in the top group. So after redealing, it should be the top card. There is. The rest on top and then the stack should go in the middle. You see what happened. As it goes to the middle, 9 cards are placed on top. The top card of the middle pile becomes the tenth card. So it was this one? What do you think about that? Pick that one up first, then grab it and place it underneath. It was the middle one, so put it underneath, now it's the tenth card. 1, 2, 3, 4, 5, 6, 7, 8, 9, boom.

Basically, you create a time card height diagram. The first time you do that is the first time you split: you have the bottom stack, the middle stack, and the top stack when you put them back together. I use 0, 1 and 2 because those are the units in ternary arithmetic. The second time is the bottom stack, you have the middle stack and the top stack, then again 0, one and two. That's the second time you've shared. And the third time you divide you have bottom, middle and top again. That's 0, 1 and two. So there are three stacks when you put them together.

This is your ones column, your 1's column. That's your 3's column. That's your 9's column. So for 15 you need two 3's, a 9, and no 1's. So it's going to be top, bottom, middle. To get 15 cards on top. And it's card number 16. BRADY: If you want to do that at home, do you have to be really good at math? MATT: There are two possibilities. You are very good at mathematics or you spend a lot of free time training your brain in this calculation method. Which is basically the same. Mathematics requires a lot of practice and developing new ways of thinking.

Then it becomes learning math or learning card tricks. In fact, you learn the same thing through it. BRADY: You said this was your favorite card trick. MATT: It is. BRADY: There are a lot of tricks. Why is this so special? MATT: People know the 21 card trick, where you always put it in the middle and at the end it's the middle card. People know this is the case, but not why. But here you already know how it works and then you can do much more with it. There is a big difference between remembering steps and knowing what to do.

And know why those steps take you where you want to be. Once you know what the steps do, you can adjust them however you want. So instead of always stopping in the middle, you can do it anywhere, because you know how it works. Because you retrieve three stacks three times, there are 27 possible arrangements to place them in the 27 positions. You can do the trick with many more cards if you want. It is the number of stacks raised to the number of divisions. If you take 10 billion cards (quite a lot) and deal 10 in 10 piles, you can get the 10 billion cards in any position in 10 deals.

Then you deal a billion cards per deck, which takes a long time. In the book Magic, Maths, and Mystery by Martin Gardner, he writes that if you make the 10 billion card version, you have to be very careful. make and count the batteries. Because if you make a mistake, no one waits for the second time. Subtitles by @Haflam