hard and easy mates
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For #1: If white to play, black loses with a smothered checkmate: 1.Nf7+ Kg8 2.Nxd8+ Kh8 (...Kf8 3. Qf7#) 3.Nf7+ Kg8 4.Nh6 Kg8 (again, ...Kf8 Qf7#) 5.Qg8+ Rxg8 6.Nf7#
Else, if black to play, the outcome is less clear. Black is clearly winning after Qxg5, but h6 is probably necessary before moving the rook off the 8th rank to avoid a back rank mate.
#2 is elementary. Rook to 7th rank, then rook to 8th rank mate.