Mathematicians say these 60-sided dice are the fairest in the world. Designing them took 15 years.

Over dinner at a gaming convention around 2010, board game designer James Ernest turned to his friend Eric Harshbarger and asked a question: Could you design a set of dice so that each player in a group — whether two people or any number — could grab one, roll and have a perfectly equal shot at going first? The rule is simple: Roll your dice, and whoever lands the highest number goes first.

The hard part is making that outcome truly fair for every player, no matter how many are at the table.

There could be no ties and no rerolls.

Harshbarger, a mathematician at Auburn University in Alabama, didn't have an answer that night.

But the question stuck.

Over the next 15 years, he and a loose network of collaborators casually worked to crack what became known as the "go first dice" problem.

Now, they finally have the answer: a set of five 60-sided dice, collectively engraved with every number between 1 and 300, with no repeats.

To mark the achievement, Harshbarger built five giant, wooden replicas of these hexecontahedrons (60-sided 3D shapes), each carved from a different type of wood.

They are now on permanent display in Auburn's new mathematics building.

The problem with dice To understand why it was so hard to crack the problem, it helps to understand the simple part.

"The easy thing is to avoid ties; you just put different numbers on all the dice," Harshbarger told Live Science.

"The problem comes in how you distribute those different numbers across the dice so that the probability is equal not only for the whole set but for any subset." That second condition is what makes the problem devilish.

Ernest's request wasn't just that eight players could roll fairly; it was that any subset of players could grab any dice from the bag roll and still have equal odds.

If five people are playing, each takes a die.