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