As stated, there are some ways to attempt a solution that strictly shouldn't be allowed (I'm sure it can be solved at least one of these ways, but I haven't worked through whether it can be solved without using the technique that shouldn't be allowed). If you made them dice instead of balls, if they were numbered, if you had stated that we had sacks or cups or such that we already knew were of equal weight, if we had a pen or other marking device that would not make a detectable change in weight on the balls, or if ...

But it is a subtle point that doesn't detract from the programming challenge (and provides alternate interpretations to make things more interesting) so I'll just leave it at that. (:

I don't know Perl6 and don't have Perl6 so getting it, learning it, and writing a solution-generator for this puzzle are more than I have time for at the moment, so I apologize for not offering or even attempting such. Thanks for the puzzle, though.