Here's an observation that might lead to a quick way to determine unique bucket combinations.
in reply to Re: Puzzle: need a more general algorithm
in thread Puzzle: need a more general algorithm
The set of bucket sizes above is the union of two sets: the set of all unique arrangements of (1 1 1 3), and the set of all unique arrangements of (1 1 2 2). The sum of the numbers is equal to the number of catagories.
This can be generalized to cover different numbers of buckets and different numbers of categories.