The only move that got out of the mess was 15.♘f6+!. Although looking very strange it does open up the g-file of Black and the white ♗ diagonal of White.

15....♙xf6 is pretty much forced: only because 15....♔h8 doesn't lead to anything better after 16.♖xf4.

16.♖xf4 is a hard to think through move, however, this is the puzzle's difficulty. Black's maybe most obvious reply is 16....♙xe5. This, as played in the game, leads to the deadly 17.♗f5!, which is the puzzle's key move: Black will not get more than a ♖, a ♗ and a ♙ for his own ♕, still having the open g-line to defend.

Any other move 16 of Black loses on behalf of the open g-file and the weak ♙s. 16....♕d7 (which seems to be the best placement) leads to 17.♕h5 (first I had 17.♖h4? ♔g7 18.♕h5 ♖h8 and Black holds. 17.♖xf6 leads also to 17....♔g7 18.♕h5 ♖h8). After 17....♔g7 the ♖ comes in, but not at h4 but at g4: ♖g4+ and Black falls.

16....♕e6 is met by the easy tempo gain 17.♖xf6 followed by 18.♕h5 which is more forcing than after Black's ♕d7.

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.
... e4:

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:

17.Rh4 was my idea, and Black seemed to be falling apart anyway. The queen sac still doesn't address the terrible lack of coordination of Black's pieces.

then I'm thinking along the lines of

15...gxf6 16. ♖xf4 fxe5 17 ♗f5
and now it looks like Black's ♕ has nowhere to go - this is all I have time for so I'm just going to look

I am far from suggesting a consensus one way or the other, but can provide an additional data point: Hiarcs 11.2MP analysis (18-ply) after <15. Nf6+ gxf6 16. Rxf4 fxe5> indicates that 17.Bf5 is much better (+3.84) than the second best move, 17.Rg4 (+2.32). But both should win.

Incidentally, this puzzle is one of more difficult ones for software to evaluate properly. For example, after 16. Rxf4, the initial analysis seems to indicate that 16...Bc8 is better (+2.56) than 16...fxe5 (+3.84).

Only human-assisted evaluation (with some sliding forward/back analysis) shows that 16...fxe5 is superior, as Bc8 ends up evaluating at (+5.84) very soon soon after 17.exf6 is entered for analysis.

At the initial position, the software initially prefers Nf2 instead of Nf6, and only after about 2 CPU minutes picks the latter.