IJPAM: Volume 74, No. 1 (2012)

THE ``52 CYCLING CARDS'' TRICK
USING MODULAR ARITHMETIC

Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa, Osaka, 533-8533, JAPAN


Abstract. Ordering 52 playing cards according to a particular rule allows one to perform a certain magic trick. By learning the rule, after viewing a given card the performer will be able to predict the next card in the deck. The key to the trick is an application of modular arithmetic, one that the author hopes will lend itself as an interesting device for mathematics education.

Received: November 29, 2010

AMS Subject Classification: 00A08, 11Z02, 97A20

Key Words and Phrases: modular arithmetic, prime numbers, primitive roots, cyclic groups, Fermat's Little Theorem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 1