Nevertheless, it's very pretty chess. :-)

It appears that the only way to defend the back rank is 35...Rc8 (as played), but then 36.Rb8!! anyway, setting up 36...Rxb8 37.Qd6+ with mate unavoidable.

35 Nf5 Qxf5

[gxf5 36 Rb8+ Ke7 ♔g7 37 ♕xg5# 37 Qd6#]

[Bxd2 36 Rb8+ Rc8 37 Rxc8#]

36 exf5 Bxd2 37 f6 Rc8 [Ke8 38 Rxd2] 38 Rxd2 h5 39 Rxd5

Now white has back rank threats, threats against f7, and has a chance to just push a queenside pawn down the board so long as black has a rook still in jail.

I like this last line, but it's pretty complicated for a Tuesday. Maybe I missed something more direct.

Black is threatening BxQe2, and 35 QxB?? allows 35...Qxd1+ and wins for Black. 35 Nf5! threatens a back rank mate and prevents BxQ. Meanwhile Qd6+ and Rb8+ are both threatened. If 35...gxf5 36 Rb8+ Ke7 37 Qxg5+ captures the bishop with CHECK and wins after either 37...Qf6 38 Qxf6+ Kxf6 39 Rxh8; or 37...Ke6 38 Rb6#
If 35...Rc8 36 Rc5 threatens the Bishop and Rook. Time to check: =====
Not very good: I missed the best defence 35...Qxf5! keeping losses down to an exchange. Black has practical chances after 36 Qd6+ Be7 37 Qxc7 Qf3!

click for larger view

<35.?>

Target: 1:25;000
Taken: slightly less than one minute, did so yesterday, no time to post.

Material: White up, ♘+♙ / ♗... for now.

Candidates: Rb8†, Nf5....hm..... <[both?]>

-ML-
A very critical position in this game. Black is down in material but is threatening the defender of the Rook on d1. White can move his Queen but this might lead to a strong counterattack by Black. A counterattack, if available, is in order. By the time I spotted <35.Nf5!> and the fact that it threatens mate nullifying the attack on the Queen, I thought it was the winning move. However, then I spotted <35.Rb8† Kg7 (35....Ke7 36.Nf5†! with 37.Qd6‡ 1-0) 36.Nf5†<>> with quite a similar position but more forced. In fact, the last line runs into the forced drawish <36....Qxf5 37.exf5 Bxd2 38.Rxh8 Kxh8 39.Kxd2 gxf5 <>> and all White advantage is gone, aside having two connected passed pawns. So, that suggests:

<35.Nf5!> but how is this so different from Rb8†? In the end this isn't with check, whilst then it is. However, no check is not a problem:

/A\
<35....Bxd2 36.Rb8† Rc8 37.Rxc8‡ 1-0> as spoken of earlier. So, Black has to counter and can do so by capturing the Knight. Yeah, or move the f-pawn, which leads to a nice mate:

/B\
<35....f6 36.Rb8† Kf7 37.Qe7†! Rxe7 38.Rxe7† Ke6 39.Re7‡ 1-0> barely, but mate is mate. Okay, the Knight:

/C\
<35....gxf5 36.Qxg5‡ 1-0> bad idea.

/D\
<35....Qxf5> so this might still be as forced as it was in the Rb8† line. The difference now, is that the Black King is still on f8. This leads to the very simple zwichenzug:

<36.Qd6† Kg7 37.exf5 > ouch. Does Black have any alternative? Yeah, Nf5 opens up one more defense unavailable in the Rb8† line.

/E\
<35....Rc8> hey, that's mean. To be honest I have been looking quite a lot longer than one minute at this defense.

<36.Qd7!> threatening the Rook on c8. 36....gxf5 37.Qxc8† Kg7 38.Qxe5† is losing, so the Rook has to retreat. Lets consider Re8 best, keeping the Rook on defense (36....Rd8? 37.Qxd8† Bxd8 38.Rxd8‡ 1-0).

<36....Re8 37.Rb7> so simple, yet intruging. Forced doesn't always win.

/EA\
<37....Re7 38.Rb8† Re8 39.Qd6† Be7 40.Qxe7† Kg8 41.Rxe8‡ 1-0>

/EB\
<37....Be7 38.Qxe8†> through the other rank :)

<38....Kxe8 39.Rb8† Bd8 40.Rbxd8‡ 1-0>

/EC\
<37....Qxd1†> desperate measures.

Not really what they were looking for (and I did look at Rb8 but doesn't Black stay in the game with Qxd1†?) but I'm guessing my line is good, right?