Their set of four “Go First” dice (pictured above) are such that when two, three or all four of the dice are rolled together:
- no ties are possible.
- each die has an equal chance of displaying the highest number.
Eric Harshbarger’s friend is Robert Ford, a mathematics professor at Dalton State College, Georgia. Initially they were considering a set of eight cubic dice, but Robert worked out that it was impossible to have a set of cubic dice that satisfied the two conditions.
He then looked at a set of four dodecahedral dice – the 12-sided dice that are used in Dungeons & Dragons – and after a week found a solution, which include all the numbers from 1 to 48 with no repeats:
Die 1: 1, 8, 11, 14, 19, 22, 27, 30, 35, 38, 41, 48 Die 2: 2, 7, 10, 15, 18, 23, 26, 31, 34, 39, 42, 47 Die 3: 3, 6, 12, 13, 17, 24, 25, 32, 36, 37, 43, 46 Die 4: 4, 5, 9, 16, 20, 21, 28, 29, 33, 40, 44, 45
Puzzler develops game-changing Go First dice | Mathematics | The Guardian