This is part of my project aiming to establish theoretical limits for bitboard based move generation in chess and similar games get as close to them as practically possible. The Hashtable Packing Problem is an optimization problem encountered when tuning Magic Bitboards in chess. Anyone trying to tackle it will have suspected that it is a hard problem, but (to my knowledge) so far no one has bothered proving that. But indeed: The abstract Hashtable Packing Problem is strongly \(\mathcal{NP}\)-co...