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White to play and win.

In terms of material black is ahead a knight for a pawn.

There are lots of candidate moves that suggest themselves (e.g., Rxf8+, Bg6, Bh7+, Rh3) but part of the problem is to find moves that really strengthen white's position. This isn't so easy (to me at least) because a lot of forceful looking moves may have the opposite effect, namely to let the black king escape the mating net in one way or another.

One of the "quieter" moves (i.e., in the sense that it is not an immediate sacrifice) is 40. Rf7. It threatens the queen and the bishop, but it also puts pressure on the g7 square and makes the e-pawn's advance a little easier.

40. Rf7 Qd8
Black's move looks more-or-less forced. Moving ...Qe8 instead allows 41. Rxg7+ and the black queen is captured next move. Moving ...Qe6 and white can either take bishop with the rook or move 41. Bf5 - a move that looks stronger to me. Then it looks like 41 ...Qh6 is the only move for black, e.g., 40 ...Qe6; 41. Bf5 Qh6; 42. Qxh6 gxh6; 43. Rxc7. Now white's e-pawn is ready to march, e.g., 43 ...Rxd4 e6 and it looks like white will win.

41. e6
If black take with ...Nxe6, then white will play 42. Bh7+ Kh8; 43. Bg6+ Kg8; 44. Qh7#. White has to be careful though because advancing the pawn also opens the b8-h2 diagonal to the black bishop.

41 ...Rxd4
(black hopes perhaps to play ...Rxd3 next with the threat of mate with ...Rd1#)

42. Rxf8+ Qxf8 (or ...Kxf8 then 43. Qf7#)
43. Qh7#

It really makes no difference if black plays something other than 41 ...Rxd4 (e.g., ...Rb3, ...Qe8, ...Bh2+, etc...) because black cannot really stop the mate. As mentioned above moving the knight or taking the e6 pawn with the knight leads to mate as well. It should also be noted that if black plays (at any time) ...Rb1+, then this is simply a spite check. Capturing the rook with the bishop does not alter anything important in the position (black is simply down a rook on top of everything else).

I do have to admit, however, that before I saw 42. Rxf8+, etc..., I looked at:

42. e7 Rxd3
(now black threatens ...Rd1# next move).
43. exf8+ Qxf8
44. Rxf8+ Kxf8
45. g3
and I think perhaps white will come out with a win with this line. But having gone back and seeing the forced mate, then this is line is not even a consideration.

Anyway, here is the best sequence (in my view), once again:

Stick with chess. Today's responders can seemingly be grouped into two categories:

1) Those who got it very quickly
2) Those who didn't get it at all

Keres was to play Taimanov, who had 9.5 points, Keres vs Taimanov, 1951.

Petrosian was to play the last placed Terpugov, E Terpugov vs Petrosian, 1951.

Geller would play Novotelnov, would was only one place ahead of Terpugov, while Smyslov would meet Aronin who had 8.5 points, Aronin vs Smyslov, 1951.

Obviously Geller, Petrosian and Smyslov would be playing for a win, and hoping that Taimanov could hold Keres to at least a draw.

1) 1. Rxf8+ and now

1a)1...Rxf8 2. Bg6+ Kg8 (Kxg6 3. Qh5#) 3. Rh8+! Kxh8 4. Qh5+ Kg8 5. Qh7# and

Fritz shows that (1.67) (20 ply) 34.Qa3 c5 35.dxc5 Qa5 36.Qxa5 Bxa5 37.Ra7 Bb4 38.c6 Rc8 39.Rb7 hxg5 40.Rxb4, will win for White.

34.Qd1? gave the advantage to Black. After 34...hxg5, White's best reply was: (-.79) (21 ply) 35.Qf3 Bd6 36.Qf5 Rb7 37.Rxf8+ Bxf8 38.Qe6+ Rf7 39.Bg6 Qb7 40.Bxf7+ Qxf7 41.Qxc6, which may still draw. However, based on his tournament position, Geller needed a win, and this may be why he tried 35.Qh5?.

However, after 35.Qh5?, the position was definitely in favor of Black: (-1.33) (21 ply) 35.Qh5? Bd8! 36.Bf5 c5 37.dxc5 Qxc5 38.Rd7 Be7 39.Bg6 Nxg6 40.Qxg6 Rb6 41.Qe8+ Kh7 42.Qh5+ Rh6 43.Qd1 Bd6.

Black then erred by playing 35...Bd6?, after which the position was equal: (.00) (23 ply) 36.Rxf8+ Kxf8 37.Qh8+ Ke7 38.Qxg7+ Kd8 39.Qg8+ Kc7 40.Qg7+ Kd8.

Geller probably saw the drawing line beginning with 36.Rxf8+, but his tournament position may have encouraged him to try 36.Rf3?. Fritz indicates the position after 36.Rf3? is in favor of Black:(-.78) (23 ply) 36.Rf3? Qa7 37.Qxg5 Rb3 38.Bf5 Qe7 39.Qg4 Rb4 40.Kh2 Bc7 41.Bc2 Rb2 42.Ba4.

Black could keep some advantage after either 36...Qa7, or (-.79) (21 ply) 36...Qb7 37.e4 g6.

At move 37, Black erred with: (.00) (21 ply) 37...Qe7? 38.e5 Bc7, after which the position was again equal.

Geller could now take the draw by playing: (.00) (22 ply) 39.Rxf8+ Kxf8 40.Qh8+ Kf7 41.Qh5+ g6 42.Qh7+ Kf8 43.Qh8+ Kf7 44.Qh7+.

Instead, Geller took a big risk and played 39.g4?. Fritz indicates after 39.g4?, Black has a strong advantage: (-1.20) (22 ply) 39.g4? Qe6! 40.Rh3 Qh6 41.Qxh6 gxh6 42.Rxh6, (-2.13) (24 ply) 42...Rb6 43.Bf5 Kg7 44.Rh5 Bd8 (-2.24) (26 ply) 45.Rh3 Rb2 46.Rd3 Bb6 47.g3 Kf7 48.Kf1 Ne6 49.Bxe6+ Kxe6 50.f4 Rb4 51.f5+ Ke7 52.Rc3 Rc4.

At this point, after either (-2.59) (21 ply) 53.f6+ Kf7, or (-2.58) (21 ply) 53.Rb3 Bxd4, Fritz shows Black's advantage continuing to increase, with good winning chances for Black.

Instead of playing the strong 39...Qe6!, with winning chances, Novotelnov blundered with 39...Rb4??, allowing a forced mate.

Geller's playing for a win at all costs finally paid off, but he still had to be content with a share of 2nd place with Petrosian, 1/2 point behind the tournament winner Keres, and 1/2 point ahead of the 4th place Smyslov.

I suggest You stick it out with Chess.

I got this one right in a matter of seconds this time. Probably because I went through a similar positional set-up only a few days ago. This happens to me, on the average, once in some 20 tries :-)

Pattern recognition! The most important aspect of the process of learning the game.

Btw, I also live in Vancouver :-)