## The Math Behind a Card Trick

Nicole Smith

To first understand what I came up with, first look at video #1 which shows the card trick itself.

Right now, you're probably wondering how I did it. To start, when I count out the cards to 26, as shown, I am able to see what all the cards are since they are face-side up. As I’m doing this, when I come upon the seventh card, I remember that card in my head, and that’s going to be the card that I predict. After counting out all those cards, I do everything as shown in the video, and then when I add up the three cards to see which card I’m predicting, that will be that seventh card I memorized earlier. It is a “self-working” trick, and all I had to do was memorize that seventh card. When first learning how to do this, I was surprised that just by remembering what the seventh card was, everything will just work itself out allowing me to “predict” what a card will be later on.

After hearing about doing these math explorations, I thought it would be really interesting to see how this card trick actually happens, and to see the math behind it. Firstly, when trying to approach how to figure this out, I was very confused. I couldn’t see why picking the seventh card was so important. I then thought about the idea that I’m always doing the same thing every time. What I mean by this, is that when I first count out those 26 cards, I put that deck below the other deck with 26 cards. This means that that seventh card is now the 33rd card since

26 + 7 = 33, and that will always be the 33rd card. I knew that this was important, but I was still a little stuck on how to start putting things together to figure out why this works. To help out,I looked at some equations that a person came up with, and I used those to help put some of my lingering ideas together. Here’s one of the equations:

10 - x = y

x = the number one of the three card represents ( so for example, if one of those three cards was the two of hearts, x = 2)

y = the number of cards that you count out the first time after picking those three cards (so if one of the cards was the two of hearts, then you would count out eight cards, which is what y represents)

Now a new variable will be added: z

z = the number of cards you count out later on (I will explain this in a video)

The new equation created will be z = x

Then since z = x I can put z into that first equation, so 10 - z = y

After, this new equation can be created 10 = z +y , which can be used to help explain why this trick works.

Now look at video #2 and I will explain what all these equations mean.

To sum up what I was explaining at the end of the video, I stated that I am first just counting out 30 cards in total (10 = z + y and then just multiplying this by 3 since there are 3 stacks of cards). Then adding an additional 3 because of the original 3 cards I count out. So in totally I am counting out 33 cards. As stated earlier, I am always counting out to that 33rd card. The whole card trick is basically tricking the audience into thinking that your counting out to a different number every time, but really you're just always counting out to that 33rd card (which you memorized earlier when it was the seventh card).

Overall, it was interesting to see how math has some part into how card tricks work, and I wonder how many card tricks are out there that are created by using math and just related to math in general.

Right now, you're probably wondering how I did it. To start, when I count out the cards to 26, as shown, I am able to see what all the cards are since they are face-side up. As I’m doing this, when I come upon the seventh card, I remember that card in my head, and that’s going to be the card that I predict. After counting out all those cards, I do everything as shown in the video, and then when I add up the three cards to see which card I’m predicting, that will be that seventh card I memorized earlier. It is a “self-working” trick, and all I had to do was memorize that seventh card. When first learning how to do this, I was surprised that just by remembering what the seventh card was, everything will just work itself out allowing me to “predict” what a card will be later on.

After hearing about doing these math explorations, I thought it would be really interesting to see how this card trick actually happens, and to see the math behind it. Firstly, when trying to approach how to figure this out, I was very confused. I couldn’t see why picking the seventh card was so important. I then thought about the idea that I’m always doing the same thing every time. What I mean by this, is that when I first count out those 26 cards, I put that deck below the other deck with 26 cards. This means that that seventh card is now the 33rd card since

26 + 7 = 33, and that will always be the 33rd card. I knew that this was important, but I was still a little stuck on how to start putting things together to figure out why this works. To help out,I looked at some equations that a person came up with, and I used those to help put some of my lingering ideas together. Here’s one of the equations:

10 - x = y

x = the number one of the three card represents ( so for example, if one of those three cards was the two of hearts, x = 2)

y = the number of cards that you count out the first time after picking those three cards (so if one of the cards was the two of hearts, then you would count out eight cards, which is what y represents)

Now a new variable will be added: z

z = the number of cards you count out later on (I will explain this in a video)

The new equation created will be z = x

Then since z = x I can put z into that first equation, so 10 - z = y

After, this new equation can be created 10 = z +y , which can be used to help explain why this trick works.

Now look at video #2 and I will explain what all these equations mean.

To sum up what I was explaining at the end of the video, I stated that I am first just counting out 30 cards in total (10 = z + y and then just multiplying this by 3 since there are 3 stacks of cards). Then adding an additional 3 because of the original 3 cards I count out. So in totally I am counting out 33 cards. As stated earlier, I am always counting out to that 33rd card. The whole card trick is basically tricking the audience into thinking that your counting out to a different number every time, but really you're just always counting out to that 33rd card (which you memorized earlier when it was the seventh card).

Overall, it was interesting to see how math has some part into how card tricks work, and I wonder how many card tricks are out there that are created by using math and just related to math in general.