ConstantImprovement: So, the basic motif of the position seems to be the following: Imagine the board without the white knight and the black pawn on f4. Then 15. Bf5 would trap the black queen.
Additional motifs that might play a role:
- A way of the rook via f4 to h4, attacking the king
- A queen move to g4 or h5, potentially
increasing the rook's pressure
- A sacrifice of the knight on f6 to make h6 a target for queen and rook
(Thinking in motifs again, imagine the declined sacrifice with the white knight on f6, the black king on h8, the black queen driven away and the white queen and rook on h5 and h4: Which famous mate could follow? Right, Qh6:+ h6: Rh6:+ Kg7 Rh7++ the bishop has g6.).
- The strong bishop that might be essential for a mate on h7 or, after Bh7+ Kh8 Bg6+ Kg8 Qh7 Kf8 Qf7:++, on f7
The whole trapping or attack must not take to long, because black will need only three typical moves to create counter pressure: c5, Nc6, d4:, targetting the d4-pawn. This must either not be allowed to happen or the attack has to be so strong that Nd4: does not matter anymore.
Then, let us try some of those:
I. 15. Rf4: is not enough, because of 15.
1. 16. Bf1 and after Qd7 the white attack will not come fast enough for the black counterplay.
2. 16. Rh4 Qh4: 17. h4: d3:, and Black should not be worse having given queen and pawn for rook, bishop and knight.
II. 15. Nf2 is basically a great move, driving the queen away from the h-file, keeping the a8-h1-diagonal closed and allowing f4: with a further f5. After Qd7 16. f4: white has attacking ideas with f5 (f6), Qh5 in combination with the bishop, and he can play Kh1 and Rg1, getting a very strong attack. Black could bring in his three counter play moves and it would be a typical race, not forcing enough for a puzzle.
III. 15. Nf6+ This achieves many things: It allows a queen trap after Rf4: and Bf5 without giving black time for counter pressure, opens up the black pawn shelter for queen, rook and bishop when accepted, and it can basically not be declined.
1. 15. ... Kh8 16. Rf4:
a. 16. ... f6: 17. Bf5 e5: 18. Bh3: f4:
19. f4: having the queen for rook and bishop with a winning attack.
b. 16. ... Qd7 17. Qh5 with a winning attack:
c. 16. ... Qe6 17. Rf6: Qd7 18. Qh5 with a winning attack (17. ... Qh3 18. Bf5 trapping the queen)
b1. 17. ... f6: 18. Qh6: Kg8 19. f6: with mate at the next move
b2. 17. ... c5 (trying to counter pressure, but too late) 18. Rh4: (Do you recognize the motif mentioned above?) 18. ... Nc6 19. Qh6:+ h6: 20. Rh6:+ Kg7 21. Rh7++
So declination leads to a winning attack.
2. 15. ... f6: 16. Rf4: This threatens Bf5 again, so the queen must move.
a. 16. ... Bc8 does not help: 17. Rh4
a1. 17. ... Qd7 18. Qh5 f5 19. Qh6: winning
a2. 17. ... Qe6 18. Rh6: winning, because the f6-pawn can not move to block the bishop-diagonal, and Qh5 follows with mate.
b. 16. ... Qd7 (16. ... Qc8 to allow Nd7 does not change anything, because this knight taking a piece at f6 will only result in f6: by white with a queen mate at g7.) 17. Qh5 winning, because of the mate threats at h7 and, after Rh4, h8.
c. 16. ... Qe6 17. Rf6: Qd7 (17. ... Qh3 Bf5 trapping the queen; 17. ... Qf6: 18. f6: is not sufficient after 19. Qh5) 18. Qh5 with mate after Qh6:. 18. ... Rc8,d8
19. Qh6: c5 20. Bh7+ Kh8 21. Bg6+ Kg8
22. Qh7+ Kf8 23. Rf7:+ (Our last motif, here with the aid of the rook) Qf7: (23. ... Ke8 24. Qh8,g8++) 24. Qf7:++
d. 16. ... e5: 17. Bf5 f4: 18. Bh3: winning
So we saw all of the motifs that we thought of at the beginning coming to life in our variations.
We came to the line:
15. Nf6+ f6: 16. Rf4: Qe6 17. Rf6: Qd7 18. Qh5 Rd8 19. Qh6: with mate in the next moves.