Answer to the Dice Problem

The number of ways of throwing n dice each with m faces is

( n + m - 1)! / ( n! * ( m - 1 )! )

where x! is x factorial, i.e., x*(x-1)*(x-2)*...*3.2.1.

Go here for the proof.


So the number of ways of throwing three cubic dice (n = 3, m = 6) is 8!/(3!*5!) = 8*7*6/6 = 56.

Are there more ways of throwing six octagonal dice (n = 6, m = 8) than there are ways of throwing eight cubic dice (n = 8, m = 6)?

One can throw six octagonal dice in 1,716 ways, and eight cubic dice in 1,287 ways (1716/1287 = 4/3).


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