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? |

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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}