After 39 Kxf6 Kg8 40 Kg6 Kf8 how about 41 Kh7!, below, (threatening 42 Rf7#).

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Black has to give up his rook to stop the mate, so after 41... Rxd6 42 Rxd6 white is ahead in material.

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Now, if 42...c2, after 43 Rc6 c1Q 44 Rxc1 Nxc1, it should be a winning position for white, because of all of those connected passed pawns.

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And yes, this is a win: 39.Rf7+! Kg8 40.Re7 and 41.Re8+ mate whatever B replies on his 40th move.

At first I was trying to mate but struggled a bit and then, because of what happened yesterday, began to look for a way to draw, which of course can be accomplished. But not being able to admit that there was no win I decided to look again for mate. All of sudden the solution sprung. I'm a little desapointed though: I took too long and almost missed it.

Time to check.

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Gosh! the "GM-missed-it-festival"!

39 Rf7+ Kg8 40 Re7+ threatens Re8 mate which cannot be prevented except by 40...Rc8 41 Nxc8 Kf8 42 Rc7 and stops the c Pawn. Visually hard to spot. 39 Rf7+ Kg8 40 Nf5 also threatens mate but loses to Ne5+ 41 fxe5 fxe5+ and Black wins. Time to check:
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Yes. Crafty End Game trainer check of the puzzle position:

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I think that the difficuty comes from the necessity to assess other factors, like here, the c3-pawn, the attack on the WN, the possibility of a check either by means of discovery or capture of the WN, etc...

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There we go.

With your line, Black can defend, reaching

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White (to play) has nothing better than 48.Kxd5 Nxe3+ 49.Ke6 Nf1 50.g4 Nxh2 draw. To win, you need <gofer>'s trick of Rf6+ and a subsequent Kg7 to promote the h Pawn.

<gofer>: congratulations on finding the win - since when is a win <a big fat zero>?

After 44. Kf7 instead of Rc7+ Black should play c2!! Now g5 Rc7+ Kf6 (otherwise just Queens as White needs to maintain threat of g6+) and now Rg7!! and the Queen is coming.

There are still tricks to find and I am guessing Aronian saw the move that Kramnik had missed and felt lucky and happy to escape with a draw and was in no mood to analyze all the way through them.

White's next f5 renews the threat of g6+ but gives up on mating with it as the pawn on f4 was controling the key square g5. Still now the threat is to march it in for a Queen of his own.

But with Nd7+ Black kicks the King away from the pawns allowing Black to Queen. Ke6 c1(Q) and as menacing as the pawns look White has nothing.

g6+ Kh6 Nf7 and Black could just walk out with Kh5 or play the dangerous looking Rxf7 where Black can keep the pawn from ever advancing that last square gxf7 Nc5+! If White takes the pawn Black checks and picks up the Rook stopping the pawn in the process. If White tries to wriggle Black wins the pawn through a series of checks. Kd6 Ne4+ Kd7 (Ke5 Qc7+; Ke7 Qc5+) Nf6 Kd6 Qa3+ the nimble knight has finally reached the right square. Kc6 Qa6+ (Ke6 Qxe3! => Kxf6 Qg5+) Kc7 Qa7+ => Qxf7.

I posted a different line than <gofer>.

He varied from the text beginning with move 39. I changed beginning with move 41. Since the f pawn is captured right away in my line, there is no need to check on f6 later.

We end up with the same position I posted earlier, below, except his line has the black king on e7, not f8.

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Embarrassing.

In my opinion, moves 38, 39 and 40 should be banned from chess, yes, altogether. After you have played your 37th move, you will write your next move down as the 41st one.

First of all, in line A of my initial post < 40... Ne5+ 41.fxe5 Rc8 (otherwise 42.Re8#) 42.Nxc8 Kf8 43.Re6...> the quick mate is disrupted by a knight move, but white still wins of course.

Second, I believe that in fact the 3rd position diagrammed by <Jimfromprovidence> is in fact won with best play by white. (Nice discovery Jim!) In my first two attempts against Crafty, I made the same mistake as <David2009>: I moved the WK towards black's d-pawn and ended with a draw. On the 3rd attempt, I noticed that the WK controls a queening square, so the correct plan is to push the passed g-pawn. Starting from Jim's 3rd diagram, I managed to win this (without consulting any endgame books) as follows:

45.g4! d4 46.ed Ne2 47.g5 Nxd4 48.g6 Nf5 49.h4 Ng7 50.Kh8 Nh5 51.f5 Nf6 52.g7+ Kf7 53.h5 Ng8 reaching the following position that might make a nice Monday/Tuesday puzzle:

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I noticed, however, that black can follow with a promotion threat 40...c2 41.Rc6 c1=Q 42.Rxc1 Nxc1 and it's kind of questionable whether white's pawns can win.

However, I noticed a big improvement: Instead of the immediate 41.Rc6, we can play 41.Rxf6+! Ke7, which not only eats a pawn with check, but it forces the black king away from the h-file , making our promotion chances much better [diagram]

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It continues: 42.Rc6 c1=Q 43.Rxc1 Nxc1 44.Kg7! [diagram]

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Black has no defence at all. The check with the knight 40.... Ne5+ is useless.