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Math Help - all possible combinations of 9 die to give a certain sum...

  1. #1
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    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
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    16
    17
    18
    19
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    24
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb 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}
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