White could make an error right off with 1.Bc3+?? when Kg8! instantly wins for Black.
Black has no choice but grab the rook since 1…Kg8 2.Nh6+ Kh8 3.Nf7+ Kg8 4.Rh8+! Bxh8 5.Nh6 is mate.
The only way to stay in the game since everything else loses trivially:
a. 2…Kg8 3.Nh6#
b. 2…Qd4 3.Bxd4+ Bxd4 4.Rh2+ Kg8 5.Nh6+ Kh8 6.Nf7+ Kg8 7.Rh8+ Bxh8 8.Nh6#
c. 2…Rf6+ 3.Bxf6+ Bxf6 (3…Kg8 4.Ra8+) 4.Rh2+ Kg8 5.Nxf6+ Kf8 6.Nxd7+
Again forced since 3…Kg8 4.Nh6#.
Trying to delay the inevitable with 4…Bh6 5.Nxh6 is pointless as mate will soon arrive on h8.
A real mistake would be 5.Rxh1? Rf4! and Black’s rook attacks from behind with abandon. After r.Rh7! Black’s bishop is frozen because of 6.Nh6 mate. It’s curious how many small mates can happen when kings are this close to each other. Of course, most games never see this variety of mating patterns which includes an attacking king because normally the king is cowering far from the action.
Now 5…Rf7 6.Nh6+ Bxh6 7.Rxf7 Be3 8.Re7! Bc5 9.Rxc7 Bf8 10.b6 wins easily. Also 5…Rb8 6.Rxg7+ Kf8 7.Nf6 and yet another pattern with mate on f7 emerges. Finally, 5…Rf4 6.Rxg7+ Kf8 7.Nf6 and wins. 5…Rf3 is essentially the same as the text.
6.Rxg7+ Kf8 7.Rxc7
The dominating position of White’s forces decides the game. The knight that gorged on the rook on h1 to start the whole line is stuck in the corner with a severe case of indigestion.
7…Rb1 8.b6! Rxb6+ 9.Nf6 Rxf6+ 10.Kxf6 Ke8 11.Rc2 (threatening 12.Rg2) Ng3 12.Ke5 and the knight is not long for this world.
8.Kf6 Rf1+ 9.Ke6 Rb1 10.Ne5! Rxb5 11.Rf7+ Kg8
11…Ke8 12.Re7+ Kd8 (12…Kf8 13.Nd7+ Kg8 14.Nf6+) 13.Nf7+ Kc8 14.Nd6+
A cute piece of geometry. By guarding b6, White keeps the Black rook at bay and initiates the final assault.
12…Kh8 13.Nf6 Rb6+ 14.Kf5 Ng3+ 15.Kg6 Rxf6+ 16.Rxf6 Kg8 17.Rf4 Nh1