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Magic Trick

When I was a kid, around 10 or so, my father taught me a magic trick using 21 cards from a regular deck of cards. Of course, I had to write a computer program to share his magic powers. Enjoy!

Rules of the game:
1. Click the "Play Game" button.
1. Pick a card from the 21 cards displayed.
2. Click on the button beside the pile your card is in. (Don't forget your card.)

MagicTrick v1.0

Since the trick depends on card counting, I'm thinking there is a mathematical proof as to why it works every time. If you know of one or want to give it a shot, let me know.

Update of Mathematical Proof (July 14, 2004)
I got an email from someone named Vicki Aka Vajoker (from somewhere in the world) with a mathematical proof for this trick. This person pointed me to the book: Mathematics, Magic and Mystery, by Martin Gardner, where he/she found an explanation of how it works.

It is not magic after all, and the explanation has to do with something called contraction maps. I guess I now know now my dad didn't use magic for this trick, but I'm at still hoping that Santa exists. I want to believe. :)

This is the theorem:

    Contraction Mapping Theorem. If (X, d) is a complete metric space and T : X -> X is a contraction mapping, then T has one and only one fixed point (i.e., there exists exactly one x belonging to X such that T(x) = x.
Aside from solving tricks, the Contraction Mapping Theorem is also used for proving the existence and uniqueness of solutions of integral and differential equations. Who said Linear Algebra is useless--Mmhh, Eigenvalues...

If you are interested in a proof, I'm sure you'll find something in google.

Source Code

One last thing
I have to clarify that when I coded the Java applet I didn't know about the Contraction Mapping Theorem. Thus, the code is stricly following the rules as they were explained to me by my dad. So the code is neither a Mathematical proof nor a direct implementation of the Linear Algebra involved. I'd think Maple would do a better job at visualizing something like this, rather than a card trick.
However, I'm still amazed how everything is connected and how a simple game can be used to explain complex mathematics.

© Jose Sandoval 2004-2009