# Re: An answer and a question

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Posted by Denis Borris on October 21, 2002 at 11:15:19:

In Reply to: An answer and a question posted by Brad Paul on October 21, 2002 at 08:44:10:

: 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?

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