# Thread: all possible combinations of 9 die to give a certain sum...

1. ## all possible combinations of 9 die to give a certain sum...

Below are all the possible values for which each individual dice hold. The die are special since they are not numbered 1-6 but have their numbers as shown below. What are all the possible combinations in which all 9 die give for a certain sum? Is there a quick way to compute this? All the possible sums are also given in the table below that-namely (x):
 Dice 1 0 0 1 2 2 3 Dice 2 0 0 0 2 2 3 Dice 3 0 0 2 3 4 4 Dice 4 0 0 0 2 2 3 Dice 5 0 0 0 2 2 3 Dice 6 0 0 0 2 2 3 Dice 7 0 0 2 3 4 4 Dice 8 0 0 2 3 4 4 Dice 9 0 0 1 2 2 3

 x Detailed list of all possible combinations? 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2. ## Re: all possible combinations of 9 die to give a certain sum...

9 dice each with 6 faces have 6^9=10,077,696 possible combinations when each 9 dice face values added we end up with only 30 sums:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}