# My direction

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Posted by Brad Paul on October 21, 2002 at 12:05:54:

In Reply to: Re: An answer and a question posted by Denis Borris on October 21, 2002 at 11:15:19:

: : Because my calculation was a numerical Monte Carlo simulation........

: good nuff: I understand.

: : My question for you. How did you do your calculation? Can you write it
: : as a nice clean expression?

: Answer question2: of course not!
: Question 1:
: As I said, I got the 197 "ways" or "number combinations" that add up to 35;
: here's a few (ascending order):
: 001: 1 1 1 1 1 1 1 4 6 6 6 6
: 002: 1 1 1 1 1 1 1 5 5 6 6 6
: .....
: 100: 1 1 1 3 3 3 3 3 3 4 5 5
: 101: 1 1 1 3 3 3 3 3 4 4 4 5
: .....
: 196: 2 2 3 3 3 3 3 3 3 3 3 4
: 197: 2 3 3 3 3 3 3 3 3 3 3 3

: Then, the "number of possible arrangements" for each is calculated:
: these 197 totals add up to 74,005,152.

: BUT I didn't calculate those myself: I sent my list of 197 to a friend with
: a FAST(!) computer: he got the results the long way: looping.

: But, Brad, I can see that if there was a way to "formularize" quickly each
: of my 197 "arrangements", we could get the results in seconds; agree?
: The same goes for the full thing: 6188 "arrangements"

: Take this one (from the above) for instance:
: 101: 1 1 1 3 3 3 3 3 4 4 4 5

: we got a number 3 times,
: another number 5 times,
: another number 3 times,
: another number 1 time.

: Is there some formula for such animals?
: If there is, we can program to count how many different numbers
: and how many times for each, then apply the formula.
: So this gigantic task would be reduced to seconds.
: What sayest thou?
Their has to be a good way to do this analytically.

I'm going to go back to looking at just 2 die then 3 etc. My thought
is that the table of possibilities is an n dimensional cube and a given
group that sums to a constant is an (n-1) dimensional cube cross
section. For the two die case the groups that sum to a constant are
diagonal rows (or 1 dimensional cubes) In the three die case the groups
that sum to a constant are diagonal planes (2D cubes).

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