ConstantImprovement: White is attacking, at first it seems like a typical sacrifical problem, but White is two pieces down. That means that
there are probably many countersacrifices to weather the storm.
The motifs that, at first sight, seem to be inherent in the position:
1. Ng5, threatening Qg7# and forcing an opening of the h-file
2. The open h-file after g5: g5:
3. The possible advance g6 after g5: g5:, with unavoidable mate by Qh8#
4. The countersacrifice Ne5: or, more probably, Nf6
5. Seen during analysis: Perhaps even 0-0-0 with moves like Rh3, Rdh1, if Black is tangled up enough that he has to allow such a White buildup.
6. A move like Qg6 and, after Qe8 by Black and Qg6: g6:, still a buildup of Rooks on the h-file, albeit this might be eventually too slow.
Since the puzzle is of the highest difficulty, there might be the possibility that there is another starting move, but White does not seem to have time for moves like Bh6 or g4.
I. 14. Ng5 g5: (the only move) 15. g5:
1. 15. ... Bg5: 16. Bg5:
a. 16. ... Qe8 17. Qh7+ Kf7
a1. 18. Rh3
a11. 18. ... Rh8 19. Rf3+ Nf6 20. Rf6:+ Ke7 21. Qg7:+ winning
a12. 18. ... Nf6 19. Rf3 (pinning the Knight) Ke7 20. Rf6: Kd8 21. Qg7: with 0-0-0, Rh1 and further pressure (or 20.
f6:+ Kd8 21. Qg7: with the same ideas), though it is not entirely satisfactory
a2. 18. Rh6 with the idea 0-0-0, Rh1 and then Qg6+, Kg8, Rh1#, but Ke7 to escape via d8 seems to defend.
b. 18. ... Nf6 19. f6:, which is decisive: The threat of f7+ Rf7: Qh8# cannot be parried adequately, for instance 19. ... Rf6: 20. Qh8 Kf7 21. Qd8:, winning.
2. 15. ... Nf6 16. ef6: Rf6: (the only move)
a. 17. f6: Bf6: 18. Qg6 (preparation for 0-0-0, Rh1, Rh8#) Bd7 19. 0-0-0 Qe8, when White has difficulty to continue the attack
b. 17. g6 Rg6: (the only move) 18. Qg6: (with the advantage of one tempo compared to line I.2.a) Bf6
b1. 19. 0-0-0 Bd7 20. Rh1 Qe8 defends
c. 17. g4 (with the idea f6: Bf6: g5 Bg5: [forced, else g6, winning] Bg5:, and the Bishop can go to f6 or h6, helping at the attack, which probably breaks through after Qg6, Ba6, Bf6, Qf8, 0-0-0 and Rh1), and moves like Rh6
do not help either after h6: and g7:.
This could be seen as our main line.
Again we saw that motifs dominate the understanding of combinations.
At the end our main line:
14. Ng5 g5: 15. g5: Nf6 16. ef6: Rf6: 17. g4 Bd7 18. f6: Bf6: 19. g5 Bg5: 20. Bg5: Qe8 21. Qh7+ Kf7 22. Rh3, with a winning attack.