Material even. White K vulnerable to mate threat with weak 1st rank. The unprotected Qc2 protects Pc3 protects Rb4 protects back rank threats. Black K vulnerable to back rank mate.

Candidate moves: Re2, Re1+, a5, d4, Re4

31...d4 32.Rxd4 [cxd Qxb4] Re1+ 33.Re1 Rxe1+ 34.Qxe1 Qxc3+ 35.Kb1 Qxh3

with the gain of a P, so capture of the Pd4 is infeasible. The Pd4 is now a queening threat and aids the mate threats either with dxc or d3 (new candidates!), so this line is in accord with the demands of the position. The only way to protect the Pc3 without material loss is

32.Rb3 Qc5

[threatening 33...Re1+ 34.Rb1 Rxb1+ 35.Kxb1 dxc and the Q eventually gets to e6 to threaten Qe7, which should be enough to win]

33.c4 Rc1 and the Pc4 falls. Time to peek (and groan at the crushing line I missed, no doubt).

So, my first line was the game line, as far as it went. Time to check the kibitzing.

However, I thought to myself--"That can't be the solution. It only wins a freaking Pawn, for crying out loud! In a Queen and Pawn endgame, no less, which are very hard to win due to the ability of the Queens to give lots of checks and maybe secure a perpetual!"

After 15 fruitless minutes trying to find a better line, I gave up--and found that the game continuation was the one I'd seen. Grrrrr.

The above is the consensus best line for white.

Now as <Terry McCracken> stated if 35 Qb3 Qd6 36 Qxc3 Qxf4 then the position is the following:

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Is there enough information to say that this is a win for black?

35. Qb3 Qxb3 36. axb3 f5!

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a) 37. gxf5? Kf7 38. Kc2 Kf6 39. Kxc3 Kxf5 and White is too slow with winning the a-pawn;

b) 37. g5? hxg5 38. fxg5 f4 39. Kc2 f3 and Black queens;

c) 37. Kc2 fxg4 38. hxg4 g6 39. Kxc3 a5 and I believe that Black wins by creating an outside passed pawn. I may have screwed up the best move order a bit but someone might want to confirm that this is a win.

So if 35. Qb3 loses, White has to mark time. Without an exhaustive calculation, a move like 35. Qe2 loses prosaically to 35...Qb4+ with the pawn ending being decisive once again after 36. Kc2 Qb2+ 37. Kd3 Qxe2+ 38. Kxe2 f5. If 35. Ka1 f5 appears to work again, with Black playing ...Qb2+ at an appropriate time.

31. ... d4 32. cxd4 ♖e1+ 33. ♖b1 ♖xb1+ 34. ♔xb1 ♕b4+ 35. ♔c1 ♕e1+

31. ... d4 32. ♖xd4 ♖e1+ 33. ♖d1 ♖xd1+ 34. ♕xd1 ♕xc3+ 35. ♔b1 ♕xh3

I just went this far and surely missed a few options.

My prefered option was the following but with very little probability to be the solution as there is no forcing moves suite in it(What ♖obins Smith ** calls a canyon). 31. ... d4 32. cxd4 32.c4 ♕c3+ 33. ♕xc3 dxc3 34. ♖b1 c2 35. ♖b2 ♖e1+ 36. ♖b1 cxb1=♕#

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Analysis by Fritz 11:

1. (-0.84): 31.Rd4-d1 Qa3-c5 32.Qc2-b3 Qc5-c7 33.f4-f5 Re8-e3 34.Rd1xd5 Re3xh3 35.Ka1-b2 Rh3-g3 36.Rd5-d4 Rg3-g2+ 37.Kb2-a1 a7-a5 38.Qb3-c4 Qc7-b8 39.Qc4-b3 Qb8-e8 40.f5-f6 g7xf6 2. (-0.86): 31.Ka1-b1 Re8-e1+ 32.Rd4-d1 Re1xd1+ 33.Qc2xd1 Qa3xc3 34.Qd1xd5 Qc3xh3 35.Qd5-a8+ Kg8-h7 36.Qa8-e4+ g7-g6 37.f4-f5 Qh3-c3 38.Qe4-e7 Qc3-d3+ 39.Kb1-b2 Qd3-b5+ 40.Kb2-c3 Qb5-a5+ 41.Kc3-b2 Qa5-d2+ 42.Kb2-b1 Qd2-d1+ 43.Kb1-b2 Qd1-d4+ 44.Kb2-a3 Qd4-c3+ 45.Ka3-a4 Qc3-c4+

c) 37. Kc2 fxg4 38. hxg4 g6 39. Kxc3 a5

You observe (very nicely, I thought) that 39...a5 is a necessary interpolation. Otherwise, 40.b4, and after dissolution of the K-side Ps, the White K must go to b4 and permit the Black K to force a standard R P draw. Unfortunately, the tempo permits the continuation

40.Kd4 h5 41.gxh gxh 42.Ke5

and both continuations favor White

42...Kg2 43.Kf5 Kh3 44.Ke6 and if the Ks don't do the shuffle, both Ps queen with White getting a check first.

42...h5 43.Ke4 and Black loses.

Instead of the obnoxious comment from which the above quote came, why don't you show how black should proceed to win? To quote myself now when commenting about 32.Rb3:

<It might be just a matter of technique, but perhaps someone can shed more insights here - engines won't provide much help, since the (expected) black win is definitely past their horizon.>

The comments from, e.g., <a q maclanahan>, <johnlspouge>, <sharkw> are an example of the discussion that I was hoping to see, but there is still no conclusion that 32.Rb3 is losing for white.

Your earlier comment, <hovik2003: After 31...d4 32.Rb3 Re1+ 33.Rb1 Rxb1+ 34.Kxb1(same is Qxb1) dxc3 white could only wait and watch how black's a-pawn advance to a4 square for final combination.> gives some indication of what perhaps might be the idea for black's win, but its credibility is lacking because of the assertion that the bad blunder 34.Qxb1 is the same as 34.Kxb1.

Here's a possible continuation after 34.Qxb1:

34. Qxb1 Qxc3+ 35. Qb2 f5! 36. Qxc3 dxc3 37. gxf5 Kf7 38. Kb1 Kf6 39. Kc2 Kxf5 40. Kxc3 Kxf4

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and white has obviously no prayer here.

after 31...d4 32.Rb3 Re1+ 33.Rb1 Rxb1+ 34.Kxb1 dxc3 with creeping bond on b2 square. If white plays best move like

35.Qb3 Qa5 36.Kc2 Qc7 37.Qxc3 Qxf4 38.Qc8+ Kh7 39.Qd7 (exchange of Queens by 39.Qf5+ Qxf5 is worse) Qf2+ 40.Kb3 g6 41.Qd3 Qc5 42.a4 a5

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Honestly, there is not anything forcing in your line. For example, instead of 37 Qxc3 white can play 37 Qa4. Now, black's a and b pawns are under attack. The position is still uncertain.

No one yet has demonstrated a forcing continuation to declare a win for black. A draw seems likely.

Meanwhile, I've been burning CPU cycles on auto-play, 22 plies/move, trying to get something out of the silicon against all hopes. So far, I got this:

Initial line that is reasonably forced: <31. ... d4 32. Rb3 Re1+ 33. Rb1 Rxb1+ 34. Kxb1 dxc3 35. Qb3>

Continuation: 35 ... Qc5 36. Kc2 Qf2+ 37. Kxc3 Qxf4 38. Kb2 h5

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and now the silly software has been thinking for 8 hours whether to play 39.a3 or 39.gxh5. The valuation of the position has been getting better for the black, and reached now (-1.63).