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F7-G7
then the queen on 8 covered by the remaining took to checkmate on G8
I don’t see a faster way
Mate starts with Rd8.
Wow, you are right, white can play 1.Rd8 first and as far as I can tell, the mate is just as short as the other one after the sacrificial delays.
1. Rh7+! Kh7 2. Qf7 Kh8 (if 2…Rg7 3. Qg7#) 3. Rd8 (if 3….Rd8 4. Qg7#) any other 3rd move, 4. Qg8# or Rg8#
The sacrificial delay that Yancey mentioned was 3…. Qf8