There is some sense of urgency here for White because Black threatens to mate with Ra1; efforts by White to prevent this with 1. Ba2 don’t help, since then Black has 1. …Rf8-b8+, 2. Bb3, Ra1# after all. So take stock of White’s own attacking resources: a bishop aimed at g8, but with its path blocked by a pawn on f7; a knight on f4, able to check the king next move on g6; a rook on the h-file; and another rook, which must not be overlooked, queued on the first rank and ready to move to the h-file once h1 becomes vacant. Once you are clear on these various sources of pressure, the germ of an idea suggests itself: a sacrifice to open the pawn cover in front of Black’s king, and then a mating attack with the pieces left over.

Experiment with checks. Starting with 1. Rxh7+ won’t work, because after 1. …KxR, 2. Rh1+, Kg8, White has a heavy piece he can drop onto h8 but no complementary piece that can add pressure on g8: his bishop doesn’t have an open line, and he can’t give check with his knight because the knight and Black’s king are then on different colored squares.

So White turns to his other check as a possible beginning: 1. Ng6+. The pawn on h7 is pinned, so Black has two choices of reply: playing f7xN or moving his king to g8. Analyze both:

(a) If Black plays f7xN, he opens a line for White’s bishop to g8. This is the signature idea of Greco’s mate, so White looks to the h-file and finds that he can mate there with 2. Rxh7+, KxR; 3. Rh1#. Remember that after Black’s original reply f7xN, he leaves a doubled pawn on g6; this is what prevents the king from escaping to g6 in reply to White’s last move.

(b) Now suppose Black replies to Ng6+ by moving his king to g8. This time a different signature move is available: 2. Ne7+, the classic prelude to Anastasia’s mate. This forces the king back to h8, and now it is just a matter of creating an attack on the h-file: 2. Rxh7+, KxR; 3. Rh1#. This time g6 is sealed off as a flight square by White’s knight, rather than by Black’s own pawn as in the first variation.