
06133123
j
2013c.00729
Nishiyama, Yutaka
Sicherman dice: equivalent sums with a pair of dice.
Int. J. Pure Appl. Math. 81, No. 1, 101110 (2012).
2012
Academic Publications, Sofia
EN
K50
K20
A20
Sicherman dice
probability distribution
generating function
factorization of polynomials
Zbl 0421.05008
Zbl 0423.60012
ME 1998d.02911
ME 1999e.03458
Zbl 0995.60504
http://www.ijpam.eu/contents/2012811/10/index.html
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, 1932 (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: trialanderror 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, 245259 (1979; Zbl 0421.05008)], as well as {\it D. M. Broline} [Math. Mag. 52, 312315 (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, 3436 (1998; ME 1998d.02911) and {\it Brian C. Fowler} and {\it Randall J. Swift}, ``Relabeling dice'', Coll. Math. J. 30, No. 3, 204208 (1999; ME 1999e.03458, Zbl 0995.60504).\}