I think as soon as you realise that white is on the verge of being mated and white has no winning defence, then the options at the other end of the board are the only way forward.

The most important part of the exchange is removing Rf8 with check as this finally frees up Nf2 from its pin.

Only at that point can white consider any kind of defence for his king...

...and only then do we see that the queen can be trapped by Nxh3 AND then attacked by Nf3!

Given that there is <no other option> for white, I don't see this as so difficult (i.e. a reasonably simple Saturday - especially if we compare it white Nxg5 hxg5 Bxg5 earlier in the week!). Also, I am not sure I agree with those that say we would not see it over the board. If you can analyse that all other (defensive) moves are losing surely you start to look at <any> other options and <Rg7+> is the only check worth looking at!

What does it say to <32 ... Nf3!>

*****

<gofer> I think Black could've won with 35...Rxf2+, but 32...Nf3 looks premature due to 33.exf3 gxf3 34.Nxf3 Qxf3 35.Bxf3 Rxf3 36.Nxf2 Be3 37.Qd8+ Rf8 38.Qxf8+ Kxf8 39.Bxd6

The more I think about it, this problem shouldn't have been too hard since the only course is to follow forcing moves or 'checks'; and in this case, the only reasonable 'check' is <36.Rg7+>

When I first started analyzing this, I first noticed the threat of ...Qxg2+. That was a tip that slow moves just don't cut it--a check is probably necessary. Analyzing in detail to see how white gets his butt kicked is a waste of time. Time spent on this is less time looking for something positive for white. So I think avoiding this analysis issue was also a big step toward finding the solution. I saw that it was losing so I moved on in search of better moves for white. In other words, don't spend a lot of time calculating how you will lose!

But with 35. ..Bh3? black missed his shot

The difficulty is the Rf8 pin of Nf2, and any attempts to shield it fail miserably. i.e., 36.Nf3 Qxg2+ 37.Ke1 Nxf3+ 38.exf3 Qxf2+ 39.Kd1 Qd2#
but if the Rf8 could be eliminated, then the black queen could be trapped with Nf3! Once I realized this, the sac line became apparent.

36.Rg7+ Bxg7 37.Qxg7+ Kxg7 38.Bxf8+ Kxf8 39.Nxh3 Nxh3 40.Nf3 winning the Q and remaining up a piece and 2 pawns.

If black tried to avoid this line and refuses the sac..

36.Rg7+ Kh8 37.Rxg5+ Kh7 38.Rg7+ Kh8 39.Rf7+ Kg8 40.Rxf8+ Bxf8 41.Qxg3+ Qxg3 42.Bxg3 leaves white up 2 pieces and 3 pawns.

The biggest surprise, after figuring all this out, is that black actually won with Bh3?? since white blundered with Qxg3.

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It's because no matter what black does he has no answer for 40 Nf3! which creates two passed pawns for white with no way to stop both.

For example 39...Ke7 (to try to catch the a pawn) loses to 40 Nf3 Nxf3 41 exf3.

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32 ... Nf3
33 exf3 Bxd2

34 Qxd2 gxf3 winning easily

34 Nxd2 Qxd3+
35 Kxf2 gxf3
36 Nxf3 Bg4

To my mind, the most difficult puzzles have numerous branches that must be kept straight and calculated accurately.. Today's puzzle is a forcing affair from beginning to end.

What makes it beautiful and difficult is the calm after the storm. If those three initial moves had forced stalemate, most of us would have seen them quickly. But to recognize the power of the relatively quiet continuation puts it into Saturday class.

So how do you find the idea in the first place? Don't ask me; I didn't solve it. But it has to be part desperation; White is so busted that any move goes straight to the Candidate List. And perhaps from musing that unpinning the ♘f2 would solve a lot of problems, realizing the 36.Nf3 wouldn't get it done, wonder if there was some way to eliminate the ♖f8, and appllying Desperation from there.

Rotstein - Zueger, Cannes 1998

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I thought White was safe after 33.exf3 Bxd2 34.Qxd2 (being able to simplify and bail out with 35.Qg5+) but 35...gxf3 is too strong

Very good!