Stable Fixed Points of Card Trick Functions
The 21-card trick is a way of dealing cards in order to predict the card selected by a volunteer. We give a mathematical explanation of why the well-known 21-card trick works using a simple linear discrete function. The function has a stable fixed point which corresponds to the position where the selected card reaches at the end of the trick. We then generalize the 21(7 x 3)-card trick to a p x q - card trick where p and q are odd integers greater than or equal to three, determine the fixed point and prove that it is also stable.
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