@article {MATHEDUC.06133123,
author = {Nishiyama, Yutaka},
title = {Sicherman dice: equivalent sums with a pair of dice.},
year = {2012},
journal = {International Journal of Pure and Applied Mathematics},
volume = {81},
number = {1},
issn = {1311-8080},
pages = {101-110},
publisher = {Academic Publications, Sofia},
abstract = {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).\}},
msc2010 = {K50xx (K20xx A20xx)},
identifier = {2013c.00729},
}