15-Year Puzzle Solved: Fair Dice Found

A team of mathematicians has designed a set of 60-sided dice that can be used to determine which player goes first in a game with any number of players, with each player having an equal chance of winning. The solution, which involves a set of five 60-sided dice with numbers 1-300 and no repeats, was the result of 15 years of work.

The problem of designing fair dice for determining which player goes first in a game with any number of players was first posed to Eric Harshbarger, a mathematician at Auburn University in Alabama, by James Ernest around 2010. Harshbarger, along with a loose network of collaborators, including Robert Ford, a mathematician at Dalton State College, worked to crack what became known as the "go first dice" problem.

The team made progress over the years, finding solutions for three and four players. A three-player solution was found within weeks, using numbers 1-18 on three standard six-sided dice. A four-player solution was later found using four 12-sided dice. Harshbarger gave talks about the four-player solution at math conferences by 2012.

However, finding a solution that worked for any number of players proved to be a more challenging task. The key to the solution was to distribute the numbers across the dice so that the probability of winning was equal not only for the whole set but for any subset of players. This condition made the problem particularly difficult to solve.

The final solution, which involves a set of five 60-sided dice with numbers 1-300 and no repeats, ensures that each player has an equal chance of winning, regardless of the number of players. To mark the achievement, Harshbarger built five giant, wooden replicas of these hexecontahedrons, each carved from a different type of wood, which are now on permanent display in Auburn's new mathematics building.

## What it means The solution to the "go first dice" problem has significant implications for game design and probability theory. The fairness of the dice ensures that each player has an equal chance of winning, which is essential for maintaining the integrity of the game. The solution also demonstrates the power of collaborative work and the importance of perseverance in solving complex problems.

## Why it matters The "go first dice" problem may seem like a trivial matter, but it has far-reaching implications for our understanding of probability and game design. The solution to this problem can be applied to a wide range of fields, from game design to statistical analysis. The fact that a team of mathematicians was able to solve this problem after 15 years of work is a testament to the power of human ingenuity and collaboration.