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    • 2013 Publication

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.
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  • Home
  • Who We Are
  • HOW TO SUBMIT
  • Past Publications
    • 2019 Publication >
      • Scientific Research
      • Mathematical Exploration
      • Scientific Exploration
      • Computer Science
    • 2018 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Scientific Research
    • 2017 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Reactions and Responses
      • Scientific Research
    • 2016 Publication >
      • Historical and Current Explanations
      • Mathematic and Scientific Explorations
      • Scientific Research
      • Reactions and Responses
      • Artistic Creations
    • 2015 Publication >
      • Historical and Current Explanations >
        • Bell Curves
        • Birds Vs. Turbines
        • Energy in the Obama Era
        • The Future of Neuroscience
        • Gender Gap in Math
        • GMOs--Yes or No?
        • The History of Minecraft: How a Swedish Indie Game Came to Dominate the World
        • The Effect of Prozac on the Brain
        • Philae Lander's Discovery of Organic Molecules
        • Advantages and Disadvantages of Wind Turbines
        • Your Own Worst Enemy: An Overview of Lupus
        • The Methylhex Ban
        • The Effect of Lyme Disease on the Immune system
        • Infectious Mononucleosis
        • Replacing CFCs
        • The Switch
      • Mathematic and Scientific Explorations >
        • The 43rd Figure
        • The Clock
        • The Collatz Conjecture
        • Constructing a Soccer Ball
        • Determining how Ballparks Affect Batter's Ability to Create Hits
        • The Rotating Conundrum
        • Pythagorean Puzzle
        • Mathematic and Scientific Explorations
        • Kinetics Lab
        • Math in the Restaurant Business
        • Math as a Vessel for Social Change
        • Sustainability of Bottled Vs. Tap Water
        • Thoughts on the Lottery
        • Understanding Player Efficiency Rating
      • Scientific Research >
        • Communicating With Computers
        • The Mystery of Asthma
        • The Nanoscopic War Against Cancer
        • Phytochemistry
        • Solving the energy crisis with Intermediate Band Solar Cells
        • A Pain That Never Ends
        • Rapamycin Resistance
        • Ampacity of a Single Core Horizontal Cable
        • Morphological Properties of Texting Acronym Formation
        • cGAS and STING Expression
      • Reactions and Responses >
        • Can Humans Survive the Climate Crisis?
        • My Experience as a Teacher's Assistant
        • Ted Talk Responses
        • Teens For Food Justice
      • Artistic Creations >
        • Chandelier
        • Deltoidal Hexacontrahedon
        • Dodecahedron Card Trick
        • Eye of the Triangle
        • Free Radric Delantic Davis
        • The Grid
        • What Does A Randomly Composed Song Sound Like?
        • Science Wing Mural
    • 2014 Publication >
      • Cover Photo
      • Artistic Creations >
        • Art Using the Fibonacci Sequence
        • Computer Generated Architecture and Designs
        • Mathematical Landscape
        • Math Art
        • Math in Music
      • Historical and Current Explanations >
        • Algae Bio-Fuel
        • An Energy Alternative
        • Clean Energy In Transportation
        • Calorie Restriction
        • Creating Energy in the Modern World
        • Dietary Intervention Impact on Gut Microbial Gene Richness
        • Earthly Applications for NASA Technology
        • Explaining Relative Motion
        • Exploring Artificial Inteligence
        • Gamma Function
        • How Leaves Work
        • Hydrogen Fuel Cells
        • Music and Brain Development
        • Programming Calculators
        • The Science of Microsatellites
        • Sci-Fi Taser
        • Sloane's Gap
        • Sustainable Energy: Why Some Ideas Shine Brighter than Others
        • Understanding The Galvanic Cell
        • The Virus: Our Unforeseen Philosopher's Stone
        • What Are Fuel Cells and How Do They Work?
      • Mathematic and Scientific Explorations >
        • Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons
        • Big Bang
        • Dictyostelium Discoideum
        • The Future of Solar Cell Technology
        • And Many More...
      • Reactions and Responses >
        • Alternative Energy Sources, New but Unused
        • An Insight Into the Curious World of Ethnobotany
        • Challenging What We Think We Know
        • The Current State of American Education
        • Discovering New Numbers
        • Interview With an Architect
        • Life of Pi Response
        • Mathematical Art Video Commentary
        • Missing from Science Class
        • The Museum of Math
        • The Inside Scoop on a Real Mathematician
    • 2013 Publication