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Message: <blockquote data-quote="Drawmack" data-source="post: 764159" data-attributes="member: 4981">Let me start by saying there is a recursive algorithm at the end for those who wish to skip the logic that brought me to that algorithm. Now on with the insanly long post.As has been previously noted this is in fact a heavily factorial problem. Question: Where do the 11 and the 4 come from?Answer: 11 = (7+5-1) = (result + set length – 1) and 4 = (5 – 1) = (set length -1)Question: Will this formula need to be modified to work with dice?Short Answer: I don’t know.Long Answer: This formula is known to with when your possible value for each element in the set is 0 – 9 (i.e. d10 where 0 = 0). So it will work on calculating the probability of a d10 if we take into account that 10 = 0 when we query for the probability of a desired number. However with dice you have can have a value for each element in the set of n, where n is the number of sides on the die being represented. Eliminating zeros eliminates a lot of possibilities and therefore means that this formula will need to be modified but this can get us working in the appropriate direction.Also this has lead me to more thinking on the idea of a recursive algorithm to solve this problem of the number of sets possible.[code][color=white]getPossibleCombinations (desiredMin,desiredMax,arySides)  thisDie = pop(arySides)  desiredMax = desiredMax – 1  possibleMax = total(arySides)  possibleMin = count(arySides)  i = 0  while((thisDie – i  + possibleMin) > desiredMax)     i++  return (thisDie-1) * getPossibleCombinations((desiredMax – thisDie), desiredMax – 1,arySides)[/color][/code]This function should yield us the number of possible combinations that will yield any result. I would still like a mathematical formula to accomplish this, but this function is easy enough to implement. That is if it’s correct.I'm going to implement this formula on a php page now, shouldn't take long, and when I'm done I'll post the link so we can all go beat up on it and see if it really works.</blockquote>

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