Meisterwerke

(a) Suppose white can castle. Ba7 is a promoted bishop. The only two squares it could've promoted on are c1 and g1. Promotion on g1 requires 6 captures, so that's 1 too many. Promotion on c1 requires only 4 captures. But two of these captures took place on the b-line, and on c1. This implies that at least two white pawns promoted, without capturing. This isn't possible, unless the d-pawn captured twice. But this means too many captures again. So white can't castle. So #2 with 1. Kd2! (Nd1~#) Qg2/Qg3/Qg5/Rb5 2. Ndf2/Qg3/Ne3/Nb2#, and not with 1. Nb2? Qg2!

(b) Now the black pawn could've promoted on c1 without capturing, so white can castle. #2 with 1. Nb2! (Kd2#) Qg2/Qg3/Qg6/Qg5 2. OOO/Qg3/OOO/Ke2#.

Solution by Philippe Schnoebelen