In looking at the puzzle position for about fifteen seconds, I saw two things: that White is threatening Rxg7+, which could be annoying, but more importantly that on material, Black is a piece up.

That immediately made me want to play 32. ... Rxf5, and if 33. Qxf5 Bd4+ would be my reply.

His response:

<32 ... Rxf5>

Everything seems to lose quickly!

Option 1

33 Re8+ Kh7 <(NOT Kf7)>

Black forces white to choose one of the options (i.e. option 4) that was available at move 33, but now Re8 is en prise and 34 Qh3+ Rh5 is simply losing...

34 Qxf5 Rxg2+
35 Kh1 Nf2+!
35 Qxf2 Rxf2 (Rxf2 Rg1#)
36 Rxf2 Qxe8

Option 2

33 Qxe4 Rxf1+
34 Kxf1 Rxe4

Option 3

34 Qb3? (or similar) Rxg2+
35 Kh1 Nf2+!
36 Rxf2 Rg1#

Option 4

33 Rxg7+ Kxg7
34 Qxf5 Rxg2+
35 Kh1 Nf2+!
35 Qxf2 Rxf2 (Rxf2 Rg1#)
36 Rxf2 Qb1+

Option 5

33 Qxf5 Bd4+!
34 Kh1 Ng3+! (34 Rf2 Qxf5 mating)
35 hxg3 Qh6
36 Qh5 Qxh5#

~~~

Yep.

I would say that you need to see the rather beautiful combination

<1 ... Rxg2+>
<2 Kh1 Nf2+>
<3 Rxf2 Rg1#>

A move that is both Offensive and Defensive: Black is a piece ahead, so trading pieces keeps the initiative. Meanwhile, White's only threat (Rxg7+) is undermined

I thought "all" replies lose, but I only considered 33.Qxf5 & 33.Rxg7+ when White has another reply: 33.Re8+ but that looks insufficient too

My computer checked (Fritz 12) refutations to 33. Rxg7+ and 33. Re8+ are:

<32...Rxf5> 33. Re8+ Kh7 34. Qxf5 Rxg2+ 35. Kh1 Rg1+! 36. Rxg1 Qxf5 with mate-in seven or less.

32...Rxf5
A) 33. Qxf5 Rxg2+ 34.Kh1 Rg1+ 35.Rxg1 Qxf5 36.Rg/exg7+ Kf8 B) 33.Re8+ Qxe8 34. Qxf5

This one took me a while, but I guess it's also because of the nature of the position. Black is up a bishop for two pawns, but more importantly is that both colors have clear threats on the king's position. White is threatening Rxe4 and Rxg7+, Black has the option of Rxg2+, clearing the bishop's diagonal for Bd4+ and possibly Rxf5.

With black to move, it's the question how he can combine his own threats whilst neutralizing white's with a single move. At first sight, the white knight plays a critical role in the white offense, and clearing it also frees the bishop's scope at the same time. This suggests <32....Rxf5!>.

It took me a while to realize what to do after white accepts the exchange sacrifice. <33.Qxf5>. Obvious is 33....Rxg2+?! 34.Kh1 but now black is in a tough spot. Basically the only thing he has left is 34....Nf2+ 35.Qxf2 (Rxf2 Rg1#) Rxf2 36.Rxf2 . With the king on h1, black lost the majority of his power and the white rooks are active. It is likely won, but I didn't want to make the same mistake as yesterday and go for the inferior continuation. Instead, black should look at the recently uncovered bishop; then it hit. After <33....Bd4+ 34.Kh1 (Rf2 Rxg2+ 35.Kh1 Rg1#) Ng3+! 36.hxg3 Qh6 37.Qh5 Qxh5# 0-1> it is turned into a forced mate instead.

33.Re8+ Kf7?! is a roundup mistake, because black 'only' goes up two pieces after the said variation. Instead Qxe8 and Kh7 look more risky but white has no play left.

White 34.:

Analysis by Stockfish 5 64 SSE4.2:

1. (-16.29): 34.Rxg7+ Kxg7 35.Qxf5 Rxg2+ 36.Kh1 Nf2+ 37.Qxf2 Rxf2 38.Rxf2 Qe4+ 39.Kg1 Qxd5

2. (-50.91): 34.Re8+ Kh7 35.Qxf5 Rxg2+ 36.Kh1 Nf2+ 37.Qxf2 Rxf2 38.Rxf2 Qxe8

3. (-#10): 34.Rxe4 Rxe4 35.Qd1 Bd4+ 36.Kh1 Rxf1+ 37.Qxf1 Qf5 38.Qb1 Qe5 39.h3 Re1+ 40.Qxe1 Qxe1+ 41.Kh2 Be5+ 42.g3 Qxg3+ 43.Kh1 Qh2#

Black 34. after <34.Re8+>:

Analysis by Stockfish 5 64 SSE4.2:

1. (-99.79): 34...Qxe8 35.Qxg4 Rxf1+ 36.Kxf1 Qf7+ 37.Ke2 Qf2+ 38.Kd3 Qd4+ 39.Ke2 Qd2+ 40.Kf3 Ng5+ 41.Qxg5 Qxg5

2. (-54.12): 34...Kh7 35.Qxf5 Rxg2+ 36.Kh1 Nf2+ 37.Qxf2

Black is up a piece. Although the position is messy and White has counterplay (attacking the knight e4 and the bishop g7), the black pieces are very active and after calculating some lines, I concluded that Black has several ways to keep the advantage. Even the strange 32...Nd2 seems to turn out well. However, the most forcing move that should be looked at first is 32...Rxf5. After 33.Qxf5, Black can go for:

- a Q+B vs R+R endgame with 33...Rxg2+ 34.Kh1 Nf2+ 35.Qxf2 (Rxf2 Rg1#) Rxf2 36.Rxf2 c4, which looks winning

- a Q+N vs R+R endgame with 33...Rxg2+ 34.Kh1 Rg1+ 35.Rxg1 Qxf5, which looks winning (e.g. 36.R1xg7+ Kf8 37.Rgf7+ Qxf7 38.Rxf7+ Kxf7 and the c-pawn just runs through)

- a mating attack with 33...Bd4+ 34.Kh1 Ng3+ 35.hxg3 Qh6+, which looks winning ;-)

Oh dear, why do I get the feeling I'm about to spend the next thirty minutes of my life analyzing this position? Chess is so hard! :)

Black appears to have one mighty shot on the board, but it is not at all easy to calculate all of the variations for me. Nevertheless, here we go!

32...Rxf5 when black wins a second piece, attacks the Qf3 hoping she will leave the defense of her King, takes the pressure off his own Bg7 and opens its long diagonal simultaneously!

If white responds 33.Qxf5 then
34...Bd4+ (Rxg2+ is not as strong due to 35.Kh1 Nf2+ 36.Qxf2 Rxf2 37.Rxf2 when black still has some work to do.)

35.Kh1 Ng3+ (Nf2+ feels more natural but is not as clear after simply 36.Rxf2)

36.hxg3 (forced)
36...Qh6# and I've already used up thirty minutes on my clock!

Now I'll quickly look at potential refutations for white on move 33.

32...Rxf5
33.Rxg7+ (After close inspection, this appears to be the only other move available to white on the entire board! How sad.)

click for larger view

White cannot recapture with the rook because of the mate threat, so after 35 Qxf5 Qe3+ 36 Kh1 Nxf1 black is ahead.

click for larger view

White can capture the knight directly or harass black's king with checks first. Black can take white's a pawn or push his own c pawn.

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32... Rxf5! diverts the Q from defense of g2 and wins by force:

When I looked at this in the morning I intended to post:

A) 33.Qxf5 Rxg2+ 34.Kh1 Nf2+! (I looked first at 34... Rh2+ 35.Kxh2 Qg3+ 36.Kh1 which appears to draw) 35.Qxf2 (Rxf2 Rg1#) Rxf2 36.Rxf2 Bd4! 37.Rg2 Qb1+ forces mate.

Oops - big flaw - the retained image error in analysis (the Bg7 is no longer there to shield the king from check). Therefore the assessment has to change to 36...Bd4??, a losing blunder. Much better is 36...Qb1+ 37.Kg2 Qd1! threatening Qxd5, Qg4+ and Bd4. This should be won by black

In any case, there is another forcing approach that is quicker:

A) 33.Qxf5 (Re8+? Kf7 34.Qxf5+ Qxf5+ 34.Rxf5+ Kxe8 wins) Rxg2+ 34.Kh1 Rg1+! 35.Rxg1 Qxf5 36.R7xg7+ Kh8 37.Rg8+ Kh7 38.R8g7+ Kh6

Now white is out of useful checks and can't defend the king.

39.Rg8 (R7g2 Nf2+ wins) Qf3+ 40.R1g2 Qf1+ 41.Rg1 Nf2#

A.1) 36.R2xg7+ Kf8! 37.Ref7+ (h3 Qf1+ 38.Kh2 Qf2+ 39.Kh1 Ng3+ wins) Qxf7 38.Rxf7+ Kxf7 39.Kg2 Ke7 40.Kf3 Nf6 41.Kf4 Kd6 wins the d-pawn and the game.

Black to play (32...?) "Medium", Black is up a piece for two pawns.

32...Rxf5! and now:

(a) 33. Qxf5 Bd4+! 34. Kh1 Ng3+ 35. hxg3 Qh6+ mates.

(b) 33. Rxg7+ Kxg7 34. Qxf5 Rxg2+ 35. Kh1 Nf2+ 36. Qxf2 (36. Rxf2 Rg1#) 36...Rxf2 37. Rxf2 Qe4+ 38. Rg2+ Kf6 and Black wins.