Perfect Shuffles through Dynamical Systems

Scully, Daniel J.

doi:10.1080/0025570x.2004.11953235

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2007

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Cited by 6 publications

(1 citation statement)

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“…Mathematics of card tricks has been a fascinating and fun subject for a long time. Ideas from number theory, group theory, dynamical systems and computer science have often been used to explain card tricks ( [4], [8], [10] and [11]). Conversely, playing cards have also been often used to illustrate mathematical concepts of probability distributions ( [9] and [12]) and group theory ( [3] and [5]).…”

Section: Introductionmentioning

confidence: 99%

Stable Fixed Points of Card Trick Functions

Champanerkar,

Jani

2013

Preprint

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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 × 3)-card trick to a p × 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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