We're beginning to nest to absurdity here - feel free to out-dent any response. :-).

I did get the idea behind the use of combinations to find a brute force solution to a randomly generated distribution. Sadly, I've written such algorithms more than once (different languages),usually for test generators. Sigh.

I just thought that what you ended up doing - looking at the structure of the problem and playing around with some possibilities would get you there faster, despite the fact that I wasn't having much success at it. Given that you felt pretty strongly that there was a sub-optimal example, I felt that you had some insight into the problem that was just escaping me (and you did).

Thanks again for the great example you came up with.

Best, beth.