I did not know I posted a comment 2 times!!!
How would you ever get to this position? The white queen is being attacked by two pieces, so why on the previous black move did black not take the queen?
My guess is black's last move to get into this position was Bd7-f5. If he had left the bishop on d7 and taken the queen with the pawn, the sequence would be 1. ... fxg6 2. Nf6+ Kf8 3. Nh7#. On the other hand, if black had played Be6 to prevent the sequence in the daily puzzle, white still has 1. ... Be6 2. Qg7+ Kf8 3. Rg1 at which point mate is inevitable.
In short, best I can figure is that Qg6 was essentially a well-calculated queen sac. That's not to mention the possibility of captures that may have been taken by Qxg6 or Bxf5.
Yes. This all makes sense. Though the 1...Be6 line should read 1...Be6 2. Qxg7+ Kxg7 3. Rdg1+ Bg4 4. Rxg4+ Kf8 5. Rh8#.
I guess the reason for 1...Bf5 would be to prevent 2. Qxg7+ because on 2...Kxg7 3. Rdg1+ black has 3...Bg6. Of course 1...Bf5 allows the puzzle solution mate in two though.
Actually, for the 1. ... Be6 line, I meant 2. Qh7+ rather than 2. Qg7+. 1. ... Bf5 would prevent Qh7+ for obvious reasons. Also, I don't think Qxg7+ really works because it gives the king more flight squares. After 4. Rxg4+, black can simply respond with fxg4 and white no longer has the mate with the knight and bishop.
Edit: Sorry, Qxg7+ does work. I guess it's been a day since I looked at this and I was thinking of a square other than g4. The f-pawn can definitely not take the rook on g4.
Queens rock up there.