In the puzzle, Black is hampered by having to stay off the d-file due to the exposed check Nxb4+ winning the Black Queen.

(1) 50.Nd5+ Ke6 51.f4 exf4 52.Nxf4+ Ke7 53.Qg7+ Rf7
54.Ng6+ Ke8 55.Qg8+ Rf8 56.Qxf8#

(1a) 51...Nxe4 52.f5 Kd6 53.Nxb4+ Kc5 54.Nxc6 Kxc6 55.Qg7

*****
Pm: I didn't see the winning line because I was overlooking 52.Qh7+: (2) 50.Nd5+ Ke6 51.Qf5+ Kf7 52.Qh7+ Ke6/e8 53.Qe7# I hope my lines hold up, or I'm in big trouble

Black threatens 50... Qxc7.

The first idea that comes to mind is 50.Nd9+ winning a full rook. But seriously, the other check 50.Nd5+ wins:

A) 50... Kd6(7,8) 51.Nxb4+ wins the queen.

50 Nd5+ Ke6 (Kd8/Kd7/Kd6 51 Nxb4+ )
51 Qf4+ Kd6 (Kf7 52 Qh7+ Ke8/Ke6 53 Qe7#)
52 Nxb4+

~~~

With 19.d5 and 20.a5 he shifts the play to the king side.

The attack on the H pawn induces the weakening 24.. h5

26.Bg5! f6 further weakens.

When i first looked at 31.a6 it appeared questionable until i realized white's 28th, 30th, and 31st were a cunning ploy to draw the Q off the 7th rank in anticipation of the intended kingside sacrifices.

not 33...fxg5? as 34.Qxh5+ leads to a powerful attack that wins the whole king side!

not 34...fxg5? 35.Qf5+ Kh6 36.Bxg5#

if 42...Ng6 43.Nc7! [with the double threats of Qxd7 and Qe6] ..Nf4 44. Qxd7+ Kg6 45. Qf5+ Kf7 46. g3 Ne2+ 47. Kh2 Rxg3 and now we can see that if the a7-g1 diagonal was open black could try to force white to draw by perpetual with ..Rxg3 since fxg3 ..Qg1+ and ..Qh1#. As this line demonstrates, it appears black can't avoid the loss of a knight, thus the game move 42.. c4 begins to make sense, opening the diagonal and eliminating the d6 pawn before it becomes a dangerous passer.

<47.Ne8!> if RxN Qh7 picks up the Q and if KxN Qc8 wins the rook. Thus 47.. Qxh6 threatening ..RxN. But it is already too late. White has 4 very nice forcing moves..

48.Nc7 Qc6
49.Qg6! (threat = Qg7#)
...Rf8 (the only move since QxN Qg7+ wins the Q)

<50.?>

This is such a puzzle where the tag 'puzzle' can make it harder than it actually is. Thinking wednesday, I was looking for an exchange or piece sac with some difficult king hunt, eventually looked at rook and queen sacs as well, but they didn't really gain anything.

In fact, the initial move is 'just' a check. I don't mind CG putting in such a position because ending a game is probably the hardest there is in chess and it does not always have to include flashy sacs and tactics. Here it does partly with the discovered check, but otherwise it's a piece coordination scheme.

<50.Nd5+> understanding Qxd5 loses, black is down to only four moves. Moving to the d-file loses the queen for at most a piece due to 51.Nxb4+. Interposing with the queen after Kd7 or Kd8 leads to more peril with forks on the f8-rook, so black's 'best' of to just allow Nxc6 but might as well resign. The last alternative is the point of the puzzle, but is just a matter of repositioning.

<50....Ke6 51.Qf5+ Kf7> Kd6 52.Nxb4+ just as much again. However, Kf7 blocks the rook interposing. This essentialy allows white to reposition his queen.

Only way to avoid the loss of his Queen is to sack his King. 50.Nd5+ Ke6 51.Qf5+ Kf7 52.Qh7 Ke6 (or Ke8) 53.Qe7#