Why wouldn't black move the rook out of danger in this puzzle instead of taking the pawn?

In this puzzle the solution is to move the pawn on f3, then black captures it with a pawn. Why wouldn't black get the rook to safety instead? I must be missing something. If black doesn't take the pawn and moved the rook instead,

* white can't move the pawn up to support the queen for a checkmate because of black's queen.
* if white takes the black pawn the king's defense is a bit opened up but the white queen is on her own there, so I don't see a checkmate…

lichess.org/training/GUq2j

This is a nice puzzle. The idea is after f5 to play f6 after black moves his rook to safety to create a mate threat on g7. If this pawn is captured Rg8 Qd8 Rxd8 is mate. So Black has to play Qf8 to defend. If The Queen leaves f8 there is Mate on g7 so when playing Rg8 there is no defense and black will get mated as he cant take the rook while Rxf8 with mate to follow is coming.
Hope this helped:)

@Flo0805, great explanation!

Rg8 – my understanding of notation is a bit patchy; wouldn't it be Rb8?

i get it.other wise it would be a checkmate or you would get the queen.

good puzzle

@Hatanga Thanks, i hope that i was able to help you aswell here:)
@slimmybim Yes, you are right

Yea the rook move was the piece of the puzzle I was not seeing

Thank you!

Yes, no matter how black tries to save the rook, after f6 it's either Lolli's mate (en.wikipedia.org/wiki/Checkmate_pattern#Lolli's_mate), Back Rank mate (with the queen controlling g7, the only conceivable escape square for the king) or Kill Box mate (en.wikipedia.org/wiki/Checkmate_pattern#Kill_Box_mate) after a few moves (black can only try to delay the mate by giving some checks with the rook they sought to save, ultimately having to give it up either way).

Thanks for sharing, it's a pretty puzzle. f5 is a discovered attack against the rook and a mate threat in one.

@Thalassokrator Why don't u have a higher rating?