Mathematical Dice Sculpture Solves Turn-Order Problem
Auburn University has unveiled a sculpture of a set of five 60-sided dice designed to determine turn order in games without ties. Each die is unique, and together they display every number from 1 to 300, ensuring that a single roll produces a distinct ranking for all players. The design required careful number tiling to make each player equally likely to go first, a challenge that took over a decade to solve.
Harshbarger previously earned a living constructing LEGO brick sculptures and mosaics before becoming a lecturer. He approached the department head directly to propose the giant dice for the new STEM complex. The sculpture features hand-carved three-foot replicas made from five distinct woods—pine, poplar, red oak, walnut, and mahogany—completed just in time for the building's opening.
The project began in 2010 with a group of mathematicians. While simpler sets for three and four players were previously devised, achieving "permutation fairness" for five players—where every possible turn order is equally likely—proved significantly more challenging. Harshbarger also partnered with a small manufacturer to sell the dice commercially.
This mathematical novelty could influence game design and fair-play mechanics in board games and competitive settings. Beyond gaming, the underlying combinatorics may inspire new approaches to randomized sorting in computational processes or statistical sampling. Harshbarger's public sculpture could spark interest in recreational mathematics, potentially encouraging students to explore complex probability problems. However, its practical societal impact remains niche, primarily affecting hobbyist game communities and educational outreach rather than broad everyday life.