Solution to Helpmate Number Four
The theme of both parts of this problem is that of selective promotion followed by self-blocking by the promoted piece. Thus black assists white by promoting to the type of piece that can rush to block the black king escaping to a certain square and thereby allowing white to construct a mating net.
(a) diagram.
Black plays 1. a1=Q and white Ne4 then 2. Qh8 Bc7 3. Qa8 Nc5 mate.
(b) Diagram but with knight on g3 moved to a1.
Black pays 1. Ka6 and white Nc2 then 2. a1=R Kc6 3. Ra5 Nb4 mate.