White to move. Can you find the fastest checkmate? 
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I can’t find it.
1. Rh8 Bxh8 2.Rxh8+ Kg7 (2..Ng8 3. Qc8#) 3. Qh6+ Kg8 4. Qh8#
I don’t think so…, 1. Rh8 Bxh8+, 2. Rxh8+ Kg7 3. Qh6#
I don’t think so…, 1. Rh8 Bxh8+, 2. Rxh8+ Kg7 3. Qh6#
!. Rh8+ Bxh8 2. Rxh8+ Kg7 or Ng8 3. Qh6#
1. Rh8+ Bxh8 (1… Ng8 2. Qc8#) 2. Rxh8+ Ng8 3. Qh6+ Rg7 4. Qf6+ Rgf7 (4… Rbf7 5. Qd8#) 5. Qd8+ Kg7 6. Rxg8+ Kh6 7. Qh4#
Some possible replies left out of some of the responees? But the right ideas.
1. Rh8+, Bxh8 (1. … Ng8; 2. Qc8 mate); 2. Rxh8+, Ng8 (2. … Kg7; 3. Qh6 mate); 3. Qc8+ (if 3. Qh6+, instead of 3. … Rg7, why not 3. … Ke8? Then 4. Rxg8+, Kd7 runs for the safety of the queenside, leaving Black’s threats against b2. Is there even a mate for White? Or 4. Qe6+, Kf8 repeats the position) Kg7; 4. Qxg8+ (if 4. Rxg8+, Kh7 delays the mate slightly), Kf6; 5. Rh6 mate looks fastest.
Unless (as usual) I’m missing something.