I have a favorite card trick that I do often because it takes no crazy card skill, just a little bit of memorization. It works through some interesting mind tricks, and I tried to figure out what makes it work, because I never learned what makes it work myself. Today, I'll go through how I figured it out. First, we'll go through the details of the trick itself. The card trick is intended for three people, but you could easily do it with just one person if you wanted to. It's a bit more impressive with three people, though. First, have your pals pick three cards. Make a pile of 10 cards, two piles of 15 cards, and keep 9 cards in your hand. Your first pal puts their card on top of the first pile, which has 10 cards. In practice, of course, their card will be face down. It's face up here to make it easier to see what's happening. Your first pal can pick as many cards as they want from the second pile (which has 15 cards) and put them on top of their card, which they just put on top of the first pile. The only restriction is that they can't take all of them. Now, your second pal puts their card on the second pile. Your second pal then takes as many cards as they want from the third pile, and places them on top of their card. Now your third pal places their card on the third pile, and you place the 9 cards that were in your hand on top of their card. Then, you put the third pile on top of the second, and that pile on top of the first. An important note is that from this new deck, make sure to take four cards from the top and place them on the bottom! Now, you start to flip cards from the deck in this order: the first one is flipped face up, the second is flipped face down, the third is flipped face up, etc. In this picture, I have done it until we reach the first card, but you would of course continue without stopping, because their cards would all be face down! Everytime you run out of cards, you pick up the pile that was made from the face-down cards, and repeat the process. When you are down to three cards, those three will be the cards your friends picked! Pretty cool stuff. But what makes it work? It sure wasn't obvious to me at first why it should always work. Because your friends can take as many cards from the other piles to place on top of their card, I at first thought that the positions of the cards changed each time. This turned out to not be true. It turns out that, when you're at the step where you would start to flip cards face up, the cards your friends picked are always in positions 6, 22, and 38 when counting from the top down. It took me some time to convince myself that this was always true; you should take some time to figure it out too! Why are these numbers significant? Well, by separating the cards into piles four times, we are essentially dividing by 2, four times. That is the same as dividing by 2^4, or 16. When we divide each of the numbers that give the positions of the cards (6, 22, and 38) by 16, and round up, we get the numbers 1, 2, and 3. These are the positions of the cards after the four divisions, which is exactly what we want. Of course, there are other numbers that satisfy this, but these numbers are the only ones that work in practice. This just gives some insight into the process. I had to apply some creative solutions when I ran into the initial roadblock of why the heck the cards were in the same position each time. I ran through the trick several times, and then I realized that giving your buddies the option of choosing how many cards they want to go on top of theirs only gives them the illusion of changing anything. It actually does nothing to affect the position of the cards, which of course had to be the case. Figuring out why is pretty funny, actually. The creative solutions I employed were simply; do the trick multiple times, and pay attention! These are definitely the simplest solutions, but they work wonders.
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AuthorPatrick Denne Archives
April 2018
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