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Sicherman dice: equivalent sums with a pair of dice. (English)
Int. J. Pure Appl. Math. 81, No. 1, 101-110 (2012).
Summary: 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 {\it M. Gardner} [Sci. Am. 238, 19‒32 (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 {\it J. A. Gallian} and {\it D. J. Rusin} [Discrete Math. 27, 245‒259 (1979; Zbl 0421.05008)], as well as {\it D. M. Broline} [Math. Mag. 52, 312‒315 (1979; Zbl 0423.60012)] in 1979. \{Editorial remark: Additional references are {\it Barry W. Brunson} and {\it Randall J. Swift}, “Equally likely sums”, Math. Spectrum 30, No. 2, 34‒36 (1998; ME 1998d.02911) and {\it Brian C. Fowler} and {\it Randall J. Swift}, “Relabeling dice”, Coll. Math. J. 30, No. 3, 204‒208 (1999; ME 1999e.03458, Zbl 0995.60504).\}
Classification: K50 K20 A20