As for how well Black played, I note that if White had exchanged on e5 rather than play 29. Qd7??, he should have won the ending without too much trouble thanks to his passed pawns on the queenside.>

Your 2nd paragraph almost (though not quite) refutes the 1st.

Czajka's 29.Qd7 indicates that he did not see it coming. I guess he thought he could somehow exchange queens, otherwise his move was completely pointless.

What would have been the sequence had he advanced his h-pawn to create an escape square?

One line:
29. ... Qg6
30. h4 Qg3+
31. fxg3 fxg3+
32. Kh3 h5
33. Nxe5 dxe5
34. Qd5 (and white has the upper hand)

another
29. ... Qg6
30. h4 Qg3+
31. fxg3 fxg3+
32. Kh3 gxf2
33. Rxf2 Rh1+
34. Kg4 f6
35. Qc8+ Kh7
36. Qf5+ (and I see a win for white)

point behind f4 as tender dig white has to recapture beet route to

his doorkeeper nod in fxg3 head above the parapet in feed him it

On the contrary: It is the fact that White played well for much of the game, and then unaccountably missed this lethal threat, that speaks of the <inconsistency> to which I referred in my first paragraph.

Black to play (29...?) "Very Easy"

Bookmarking this so I can print out for my students. (I often skip Mondays.)

I think you deserve a better answer than you've had up to now. So let me try ...

This is the position just before both players missed the Qg3+ mate.

click for larger view

It's white to play.

He looks to be pretty safe. The focal point for the black attack seems to be g2, but white can't aim another piece at that square. White seems to have made a fortress on the kingside, which means that he is free to hoover pawns on the queenside.

Neither white nor black have a sense of danger at this point because the Qg3+ combination doesn't work yet. What is more, g3 seems a very unlikely entry square for the queen because it is well guarded. Black just doesn't have enough pieces in the attack. Let's call it defcon 4.

Now white decides to trade off a pair of pieces - standard practice when up in material. So he plays the disastrous 26. Nxe5. He doesn't see that this drags the black bishop to e5, which means that Qg3+ becomes playable.

This is the position that black finds himself in a couple of moves later ...

click for larger view

The dynamics have changed, but it was white who changed them and not black. White pulled the black Bg7 onto the e5 square. That means that black hasn't fully analysed the consequences of that change - because he didn't choose to make it.

It is much easier to see a combination if you have analysed it and prepared it. It is much harder if your opponent plays the first part of the combination for you.

In the POTD, we get none of this. When we first analyse, we don't see the moves before the puzzle. We don't get the benefit of being part of a sustained attack. But equally we don't get the disbenefit of looking in the wrong place when the dynamics of the situation suddenly changes.