Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dice Combinations for a Particular Sum

  1. Aug 27, 2008 #1
    Okay, here is a problem that has been bugging me:
    I'm not necessarily looking for a general solution, though one would be great. But I would like to at least be able to compute the answer for particular sets of input.

    So far, I believe I have found that answering the main question is equivalent to determining the number of (rn) -combinations in a multiset with the form

    {{k1, ... , kn}, {(k1, d−1), ... , (kn, d−1)}}

    Basically, starting with each die at one and counting the number of ways I can build up to the total, r, without exceeding d in any of them.

    I can find a solution where d = ∞ easily enough, but I am not sure how to eliminate the illegal combinations from that using Inclusion-Exclusion.

    If someone could help me finish my solution or propose an alternate, easier solution, I would be very grateful.

    Basically, if we are using two six-sided dice, then there are six ways to add up to seven:

    1+6, 2+5, 3+4, 4+3, 5+2, and 6+1.

    And five ways to add up to eight:

    2+6, 3+5, 4+4, 5+3, and 6+8.

    Et cetera.
    Last edited: Aug 27, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Dice Combinations Particular Date
B Simultaneous roll of Non Transitive Dice Oct 16, 2017
I Probability involving n dice Apr 26, 2016
Predicting the correct dice Nov 22, 2015
Combination formula on dice and bit errors Mar 29, 2015
Number of combinations of 30 dice rolls Mar 24, 2012