White to play and mate in three moves:
1.Kd7?
No...
Rh4.
1.Kd7 e6 2.Qh7 Kf8 3. Rxf6++!
After 1...Kg7 or 1...Kg8 there is no mate in three.
Rg4.
Correct! Followed by Qh7 and Rg8 mate.
If d6 Qh7+ then mate.
Same result if Kf8 or Ke8.
If d6 Qg7+ then mate.
2.Qh7+
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White to play and mate in three moves: