Balanced Non-Transitive Dice
نویسندگان
چکیده
We study triples of labeled dice in which the relation “is a better die than” is non-transitive. Focusing on such triples with an additional symmetry we call “balanced,” we prove that such triples of n-sided dice exist for all n ≥ 3. We then examine the sums of the labels of such dice, and use these results to construct an O(n) algorithm for verifying whether or not a triple of n-sided dice is balanced and non-transitive. Finally, we consider generalizations to larger sets of dice.
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