As a player rather than a specialist problemist, I usually find three- movers too difficult. The joy of solving is not worth the effort expended, but the witty key move makes this one an exception.
Black's king looks well surrounded, but getting at it is no easy matter, particularly when it can dart round the corner to g4 and h3 if necessary. Looking first at Black's moves, we can see that most have mates provided for them: Any knight move allows Ne3 mate; Bg4 is met by Ng3 mate, while Bxg6 allows 2. Rxf3+] exf3 (or Kg4 3. Nh2) 3. Ng3 mate; and Rd5 or Rxc5 allow the elegant 2. Qxe4+] Kxe4 3. Ng3 mate.
The difficult one to overcome is 1 . . . Kg4, when 2. Nh2+ Kh3 3. Nf4 allows Kxh4, while 2. Rxf3 Kxf3 3. Nh2 offers escape with Ke2. Crude attempts such as 1. Qxd2, 1. Qxd6 or 1. Bxe5 do not deserve to succeed. They fail to e3, Bxg6 and Kg4 respectively.
The key to solution is providing a mate after 1 . . . Kg4 and the right idea comes from a surprising direction. The first move is 1. Ba4] with the principal new variation 1 . . . Kg4 2. Rxf3] Kxf3 3. Bxd1 mate.
After 1 . . . Kxg6 2. Ng3] the bishop will return to e8 to mate next move, which is also the finish after 1 . . . Nc3 (or other knight move) 2. Ne3+ Kxg6 or 1 . . . dxc5 2. Qxe5+ Kxg6. Other mates are mostly unchanged from before.
With everything apparently going on in the area around the black king, the key move is delightfully disguised, especially in view of the blockage on the a4-d1 diagonal.
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