Math in the Middle Institute Partnership


Date of this Version



In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Gordon Woodward, Advisor July 2009


Many different types of games involve the use of numbered dice. The most common type of die used is the standard six-sided die with the numbers one through six used on its six sides. What if there was another way of numbering a set of dice (using only positive integers) that would create the same probability outcomes as those of a standard set of dice? The February 1978 issue of Scientific American reports that George Sicherman discovered such a numbering (Broline, 1979). Sicherman discovered that two cubic die numbered 1-2-2-3-3-4 and 1-3-4-5-6-8 have the same sum probabilities as do the standard set of cubic dice (both labeled 1-2-3-4-5-6). This paper will explore his findings.