Steve Witham showed 17 shots is optimal for n=10, and wrote:
I know solving cases by brute force is useless but I was sort of hoping to see patterns or something! Or, in the course of inventing optimizations, to get some insight. I don't feel insightful yet.
It wouldn't be too bad if the optimal solution isn't always generalizable. So far we can do p^k and 2p^k in general with 2n-1 shots; if it's always possible to achieve 2n-1, for example, then that's a great result even if it's not always tight. So perhaps the thing to do with your program is not to search for the minimal solution for n=12, but for *all* solutions with up to 23 shots, and see if we find anything that looks generalizable -- maybe it will lead us to a 2^j p^k solution. (I'm still annoyed that I can't *prove* 2n-1 is minimal even for primes, but that's another story.) --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.