This is an old puzzle from the book of Phillip Stamma(1737) who is a strong player of his time and also the creator of the notation that we use.

Why couldn't black play Qf5 to get out of trouble?

yeah posible. 1700's thought is not like today. As i said it is an old puzzle. But i think black is giving the rook after Qf5 , by same like of aproach. 2.Nf7+ ... RxN (if ..Kg8 Ne7#) QxR

bizimtansu wrote: yeah posible. 1700's thought is not like today. As i said it is an old puzzle. But i think black is giving the rook after Qf5 , by same like of aproach. 2.Nf7+ ... RxN (if ..Kg8 Ne7#) QxR

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after 3. QxR .. Nb8xNc6 so it would be rook for two knights

4. Rxc6 looks like it could get white into trouble, but i'd need to spend longer than i want to looking at it (there's the threat of Qf3+ to win the rook and also to push the pawn for promotion if the white queen defends the rook)

Qf5 fails to Ne7, which threatens checkmate (Ng6#) if the queen moves off g6 and Qg8+ followed by Nf7# if that threat isn't covered.  The knight checks only buy black some time.

The knight check coupled with that passed pawn buys tempo to get the queen out then take the knight threatening mate with the pawn on f6. 

Can someone run it through their chess analyser and see if there's a forced mate?