IJPAM: Volume 81, No. 1 (2012)


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

Abstract. George Sicherman discovered an interesting pair of dice whose sums have the same probability distribution as a pair of standard dice, and this was reported by Martin Gardner in 1978. This pair of dice is numbered, 1, 3, 4, 5, 6, 8 and 1, 2, 2, 3, 3, 4, and is unique. In order to prove the uniqueness of his combination three methods are shown: trial-and-error with pencil and paper, a Visual Basic program, and factorization of polynomials. The third is the most elegant solution and was presented by Gallian and Rusin, as well as Broline in 1979.

Received: July 16, 2012

AMS Subject Classification: 11A02, 00A09, 97A20

Key Words and Phrases: Sicherman dice, Probability distribution, Generating function, Factorization of polynomials

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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: 81
Issue: 1