Are Stupid Dice Necessary?

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Abstract:

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3, . . ., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7. 8, . . ., 70 occur equally often. We investigate such relabelings for pq-sided dice, where p and q are distinct primes, and show that these relabelings usually involve stupid dice, that is, dice with the same label on every face.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/college.math.j.44.4.315

Publication date: September 1, 2013

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