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Cards, codes, and kangaroos. (English)
UMAP J. 32, No. 3, 199-236 (2011).
Summary: The Kruskal Count is a card trick invented by mathematician (not magician) Martin Kruskal. The mathematics of the trick illustrates Pollard’s kangaroo method, which was designed to solve the discrete logarithm problem: Given a finite cyclic group, $G=\langle g\rangle$, and $X\in G$, find $x\in{\bbfZ}$ such that $g^x=X$. In this Module, we demonstrate the card trick and in revealing its secret, we uncover connections to the discrete logarithm problem, cryptography, and Markov chains. Prerequisites for this module include: Cyclic groups, generators, modular arithmetic, matrix inverses, modular arithmetic and factoring functions for a computer algebra system (e.g., for Maple, the functions mod and ifactor, if ‒ then statements and for ‒ loops in programming in such a system, expected value, and standard results about Markov chains (transient and absorbing states, canonical form of the transition matrix, and the fundamental matrix).
Classification: M95 H45 K65