Both Nh6+ and Qxf8+ seem either useless or losing.

37.Nf6+ Bxf6 (37...Kh8 38.Qh2+ Bh6 39.Qxh6#) 38.gxf6

This threatens 39.Qxf8+ Kxf8 40.Rd8#. Black has useless checks on a1 and d1, but I don't see a decent defense for black.

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34.Qd6,
This is good, but it is not the only move for White in this position.

[The box likes: (>/=) 34.Kg2, here for White, and so do I. (34.Kg2, a slight plus for White - Fritz 11.) ]

34...g6!?; (Is this necessary?)
I am not even sure about this move, it does weaken the dark squares a lot. (However, Bacrot was in zeitnot here, and maybe was worried about Leko eventually playing g5-g6. My first impulse was to play 34...Qb3; in this position.)

However, after checking things with the box, it seems that "the iron monster" agrees with Bacrot, 34...g6 might be forced (or best).

35.Nh2!?, (hmmm)
This gives White a win, but probably was not the best move for White.

[Better was: >/= 35.Qc5, with a slight plus for White, - Fritz 11.]

35...Bc3;
The best move here for Black.

36.Ng4 Bg7?; (Really - '??')
Black throws away a pretty decent position with this one errant move.

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Now we have reached the position for ChessGames P.O.T.D. ("Problem of the Day.")

[After the following moves: >/= 36...Qxb4; 37.Qxb4 Bxb4; 38.Rxa7, (with an advantage) I think that it would be problematic (at best!) for White to win - from here. ]

White to play and make his 37th move in this position.

37.Nf6+,
Sometimes the most direct move is the best move.

[Less effective would be: </= 37.Kg2?! a5; 38.Rd8±.]

37...Bxf6[]; (Box.)
This is completely forced.

[Of course not: </= 37...Kh8??; and now 38.Qh2+, ( ) and it's mate next move. ]

38.gxf6, (The most aggressive.)
This is the best move for White.

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Now White has many threats. You have to be a pretty decent player to see that White threatens a simple win here: 39.QxR/f8+!, KxQ/f8; 40.Rd8#.

In this position Black should play ...Re8. Another (less obvious) win would be: 38...Re8[]; 39.Qe7!, RxQ/e7; Black may as well take, to retreat to f8 allows QxR+, winning.) 40.fxe7, and Black cannot prevent White's pawn on e7 from promoting.

[</= 38.Qxf6? Qxb4; 39.Rxa7, "="]

Now Black is quite lost, however Fritz shows that playing the Rook to e8 was the only decent try for Black.

38...Rc8!?; (Maybe '?!' or '?') 39.Rxf7!,
Black resigns. (Taking the Rook allows Qe7+ and mate next move.)

1-0

to reiterate the remainder of Dzechiel's solution...

39.♕e7! (39.♖e7?! ♖f8) 39...♖xe7 40.fxe7
♕a1+ 41.♔g2 ♕e5 42.♖d8+ ♔g7 43.e8=♕

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What follows is 37…Bxh6 38 gxh6 Qa1+ 39 Kg2 (all look forced), then 39... Re8 (to prevent h7+)

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Now 40 Qf4 (threatening Qxf7) Rf8 (forced) 41 Rxa7! (If 41…Qxa7, 42 Qf6, winning the queen) Qd1 42 Ra5 Qd5+ 43 e4 Qd4 44 Rxb5.

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What I found was that if black doesn't play Bg7 then white can even not play Nf6 and instead dance around the black king (if black takes the Knight when it moves to f5 then it gets caught with Qh6+ Kg8 g6 mating!), so we might get...

36 ... Qa1+
37 Kg2 Qb2?/a6?

38 Nh6+ Kg7 (protecting the rook)
39 Nf5+ Kg8 (protecting the rook)
40 Ne7+ Kg7 (not allowing Qh2+ mating)
41 Nxg6 Re8 (there could be better but lets assume not...)

42 Ne7 Kf8 (to avoid Qh6#)
43 Nf5+ Kg8 (forced)
44 Nh6+ Kh8 (to avoid Rxf7+)
45 Nxf7+ Kg8 (to avoid Ne5+ mating)
46 Nh6+ Kh8 (forced)

So the knight has cleared all blacks defenses...

:-)

I agree with the first part; however the 2nd part (an idea that I looked at too) doesn't work (with WQ on h2 or h6) because of Qa1+ then Qxf6.

<Jimfromprovidence>

An interesting and different (if longer) approach, and your analysis looks solid. It's worth noting that 39... Qh8 (instead of Re8) loses to Qxf8+. Not surprising that white has more than one way to win with such an advantage.

<..<dzechiel>'s post is spot on...!>

White to play (37.?) "Medium"

I only had one candidate move, and I found the winning idea right away.

37. Nf6+ (pretty obvious, but it's the follow-up that matters) Bxf6 (forced, or mate follows after 37...Kh8 38. Qh2+) 38. gxf6

Now White threatens 39. Qxf8+! Kxf8 40. Rd8#, so Black must move the rook.

A) 38...Qa1+ (this can come later as well) 39. Kg2 Re8 40. Qe7! (better than 40. Rd8 Rxd8 41. Qxd8+ Kh7 42. Qe7 Qa2 43. Qf8 Qd5+, which draws) Rxe7 (or 40...Rf8 41. Qxf8+) 41. fxe7 Qe5 42. Rd8+ Kg7 43. e8=Q and wins.

Leko vs Bacrot, 2009 (37.?)

White to play and win.

Material: N for B. The Black Kg8 has 2 legal moves, both on the h-file. The White Qd6, Ng4, and Pg5 attack the weak dark squares around Kg8, defended only by the Black Bg7 in the complete absence of the Black Qa4. The White Rd7 attacks Pf7, which Ng4 can attack in 1 move. The White Kg1 is vulnerable to the checks Qa4-a8+ or Qa4-d8+, which the White battery on the d-file presently defends, but even without the defense, perpetual check is unlikely.

Throughout the following, Black can interpose [1]…Qa1 [2]Kg2, to no avail.

Candidates (37.): Nh6+, Nf6+

37.Nf6+ Bxf6 [Kh8 38.Qh2+ Bh6 39.Qxh6#]

38.gxf6 (threatening 39.Qxf8+ Kxf8 [Kh7 40.Qg7#] 40.Rd8#)

(1) 38…R to between c8 and a8

39.Rxf7 (threatening 40.Rg7+ 41.Qh2#)

39…Kxf7 40.Qe7+ Kg8 41.Qg7#

(2) 38…Re8 39.Qe7 (threatening 40.Qxf7+ 41.Qh7#)

39…Rxe7 [Rf8 Qxf8+ again]

40.fxe7 (threatening 41.e8=Q+ or 41.Rd8+ 42.e8=Q)

Less obvious is the Rook sacrifice, which I missed (and did not see the followup for until I read earlier posts). I instead found another move which appears to be just as resignable as White's actual move, and with the bonus of being one of those venomous quiet moves that always have a certain beauty to them:

39 Qf4!

<zanshin> considered this, and then wondered if White had time for this. The answer is indeed a resounding yes, however, the immediate threat is not yet 40 Qh6? (which would lead once again to the same fork Qa1+ that thwarts 39 Qh2?) but instead a lethal in-between move: 40 Rd6!!

In other words, White does not immediately threaten Qh6 - he instead *threatens to defend*! 40 Rd6!! would protect the f-pawn, making the threat of Qh6 real. At this point Black cannot flee with the King, since 40 ... Kf8 allows 41 Qh6+ Ke8 (or Kg8 42 Qg7#) 42 Qh8#, while 40 ... Kh7 falls to 41 Qh4+ and 42 Qh6, with mate to follow.

Therefore, Black cannot allow Rd6 without losing his Queen (as it would have to be given up for the f-pawn, after which he would probably still succumb to mate, just as if he gives up the Queen for the f-pawn after the actual 39 Rxf7). The question then arises as to whether Black has a suitable way to prevent this threat.

The answer would seem to be no:

39 ... Rc6 (to challenge the Rook; 39 ... Rc4 to drive the Queen fails similarly) 40 Rd8+ Kh7 41 Qh2 does the honors.

39 ... Rc1+ 40 Kg2 and Black has no good continuation, being threatened with both 41 Rd8+ and 41 Rd6.

39 ... Qa1+ 40 Kg2 and Black still hasn't come up with a more permanent way of preventing Rd6, nor is Rc6 viable here either.

"Your" move, 39.Qf4, does NOT work!

I spent a few minutes with Fritz 11, and here is what I came up with:

</= 39.Qf4? Qa2!; 40.Rd6!? Qb1+; 41.Kg2 Qf5; 42.Qxf5 gxf5; 43.Rd5, <(A plus over an equal sign.)>