I've been trying to visualize this position for the past 10 minutes and I'm still wondering what white's best continuation is...>

That was very stupid of me...after

31...Nxd6
Then I got bogged down working out variations arising from: 32.Qc5 OR 32.exd6+

-- 1/2 CREDIT.

I don't recall who said (Kotov, I think, possibly quoting Tal) ...it's a mistake, a waste of valuable time, to calculate variations beyond the point you are convinced you've found the best move.

It's good advice I think... The opponent must choose one variation. The calculation of which variation is the best one to take is the opponent's'headache, not ours!

A puzzle is a bit different though, I admit.

I'm sort of shocked that Colovic missed 33.Qa8 ... that's the clearest winning line and shouldn't have been too hard to find OTB at that point.

The continuation from the resignation position is quite an eye-opener...

2) Make sure copy/paste actually works.(it won’t if you’re using Firefox);

31.Bd6+ Kb6 32.Bf3 Ra7 33.Ra5 Ka5 34.Ra1+ Kb6 35.Qc5+ Nxc5 dxc5# (pls. correct me if i'm wrong!!!)

Part I of the analysis:

Nice position today, surely not White to play and draw. Many candidates, at first glance only e6 and Bd6+ seem to promise something.

Let us start with the more forcing

I. 31. Bd6+

I.1. Declinations

I.1a. 31. ... Kd8 32. Qb7:
I.1b. 31. ... Kb6 32. Bf3 (Threat: Qb7:#) and either 32. ... Nd6: 33. Qd6:+ Bc6 (33. ... Ka7 34. Qc7#) 34. Qc6:+ Ka7 35. Qb7# or 32. ... Nd8(c5) 33. Qc5(:)#.

That means that Black has to take the Bishop.

I.2. Taking the bishop

I.2a. 31. ... Rd6: simply loses the exchange without compensation

I.2b. 31. ... Nd6: Critical position, there are many possibilities now.

I.2ba. 32. d6:+ Rd6: (Black can't afford to let that pawn live, see: 32. ... Kd8 33. Qb7 Rd6: 34. Ra5: ; 32. ... Kb8 33. d7 ; 32. ... Kb6 33. Qc5+ Kb7 34. Qc7+ Ka8 35. Bf3+ Bc6 36. Bc6:+ [36. Ra5: seems to be one move faster: 36. ... Ra5: 37. Bc6:# or 36. ... Bf3: 37. Ra6:#] Rc6: 37. Ra5+ Ra6 38. Ra6:#) Now what? 33. Re7+ Ne7: and I see no further continuation, since 34. Qc5+ Nc6 (34. ... Rc6 35. Qe7:+ Kb6 36. Qd8+ Rc7 37. Qb8+ Rb7 38. Qd6+ Be6 39. Bd7 Rc7 40. Ra5: Ka5: 41. Qc7:+ Ka6 42. Qc6:+ [42. Bc6: Qb8 43. Qf7 and I would say this is unclear, rather better for Black] Ka7 43. Qb5: Qb8 44. Qc4:, which I would rate as advantageous for White because of the pawn passed pawns.) seems solid, unless ... 35. Ra5: could bring additional pressure. There are many possibilities in that position, moves like Kb7, Qf8 and Bd7.

When nothing else suffices, I will return here.

33. Qc5+ Rc6 (Bc6 34. Ra5:, with is better for White because the threat 35. Ra7+ is very strong) and now 34. Re7+ Ne7 35. Qe7:+ transposes to our long line in the brackets already given above. Somehow I don't like that line, in the first place because it seems, despite many moves being forced, to be too long and inconclusive for a Friday, and furthermore because every long variation is prone to more and more errors. There is an elegance in the hunt of the king, which resembles a triangle, for there is no clear finale. What about 34. Qa7+? 34. ... Kd8 35. Qb8+ Rc8 36. Qc8:#. 34. ... Kd6 35. Qb8 Rc7 (35. ... Kd5 36. Bf3#) and now? 36. Ra5: Bc6 seems to hold. 36. Qd8+ Bd7 37. Qf6+ Be6 (Kd5 36. Bf3#) 38. Ra5: (Black's position seems to be nearly falling apart.) Rc6 39. Rb5: Qd8 and Black seems to hold the balance.

That means: 32. d6:+ is a mistake.

Part II of the analysis:

So, since 32. d6:+ is wrong, now another try:

I.2bb. 32. Ra5: (much more puzzle-like: That little finesse somewhere in the middle.)

Acceptance first: 32. ... Ra5: 33. Qd6:+ Kb7 34. Bf3+ Ka7 (Bc6 35. Qc6: and 36. Qb7#) 35. Qc7+ Ka6 36. Qb7#

Declination 1: 32. ... Rb6 33. d6:+ (Letting the pawn live does not save Black: 33. ... Kd8 34. Ra8+ Rb8 35. Rb8:#; 33. ... Kb8 34. Ra8#) Rd6: 34. Ra7+ and 35. Qa8#.

Declination 2: 32. ... Rc6 33. d6:+ and now only the other moves: 33. ... Kd8 34. Ra8 Rc8 35. Rc8:#; 33. ... Kb8 34. Qb5: Rb6 35. Qb6:#.

Declination 3: 32. ... Ne7 (Idea: 33. Ra6: Nd5:) 33. d6:+ Rd6: 34. Re7:+ with some short mating lines.

Declination 4: 32. ... Nb7(c8) 33. Ra6: and clearly

Conclusion:

The solution is: 31. Bd6:+ Nd6: 32. Ra5: and now the acceptance as the main line: 32. ... Ra5: 33. Qd6:+ Kb7 34. Bf3+ Ka7 (Bc6 35. Qc6: and 36. Qb7#) 35. Qc7+ Ka6 36. Qb7# All declinations do not work,see Part I.

32. d6:+ is much more complex, but much less clear, since after 32. ... Rd6: 33. Qc5+ Rc6 there is either 34. Re7+ Ne7: 35. Qe7:+ with a long variation resulting in an endgame where White is an exchange down and many pawns up and might have a certain advantage, or 34. Qa7+, where Black seems to hold the balance after 34. ... Kd6 35. Qb8+ Rc7 36. Qd8+ Bd7 37. Qf6+ Be6 38. Ra5: Rc6 39. Rb5: Qd8.

Okay, so they are a couple of superb white bishops. The queen is just a monster, and the black king is completely lost in the abyss. White also has magnificent dark square control on the queen-side. It is time to utilize these advantages to smash up the black king.

Considering all these advantages, the first candidate I considered was:

<31.Bd6+> and I think it is winning.

White doesn't mind giving up one of his powerful bishops, if it means black is forced to part with one of his dark square defenders.

If we rule out 31...Kd8 32.Qxb7 , that leaves three possible defensive moves:

<A> <31...Kb6> <B> <31...Nxd6> <C> <31...Rxd6>

I will deal with each of these in turn:

<A> <31...Kb6 32.Bf3>

Threatening 33.Qxb7#. If now 32...N anywhere 33.Qc5#. So that forces

<32...Ra7>

White now continues to exploit the dark squares:

<33.Bc5+>

If now 33...Nxc5 34.Qxc5+ Ka6 35.Rxa5+ Kxa5 36.Ra1#
If now 33...Kc7 34.Bxa7 .

<33...Ka6>

34.Bxa7 now wins in two more moves, but I prefer the rather more flashy

<34.Qxb7+ Rxb7> blocking the king <35.Rxa5+ Kxa5 36.Ra1#>.

So option <A> loses.

What about option <B> <31...Nxd6>?

<31.Bd6+>, and now option <B> <31...Nxd6>

<32.exd6+>

All king moves now lose, eg.,:

32...Kd8 33.Qb7, with indefensible mate threats on c8 and c7 .

32...Kb8 33.Qc5 (threatening 34.Qc7+ Ka8 35.Bf3 ) 33...Bc6 34.Rxa5, and black can no longer cope with the pounding (if 34...Rxa5 35.Qb6+ and mate will come shortly) .

32...Kb6 33.Qc5+ Kb7 34.Qc7+ Ka8 35.Bf3+ game over .

So black has to play

<32...Rxd6>

However, now the a5 pawn is unguarded, and the a1 rook will soon enter the fray.

<33.Qc5+>

Black cannot now play 33...Rc6, which leads to a forced mate with 34.Qa7+ Kd6 (34...Kd8 35.Qb8+ Rc8 36.Qxc8#) 35.Qb8+ Rc7 (35...Kd5 36.Re5+ Nxe5 37.Qxe5#) 36.Qb6+ (36...Kd5 37.Bf3#; 36...Bc6 37.Qc5#; 36...Rc6 37.Qd8+ Bd7 38.Qxd7#.

So unless black wants to give up the rook, that leaves

<33...Bc6 34.Rxa5>

Black must now meet the threat of 35.Ra7+ Kb8 36.Qb6+ Bb7 37.Qxb7#. The only way to do that without an immediate loss of either the black bishop or rook is

<34...Qb8> which guards b6 and indirectly the guards the d6, rook which would have been hanging after 35.Ra7+ Kd8

However, now all the black queenside pieces are inadequately guarded, and black soon succumbs to the constant pressure

<35.Ra7+ Kd8 36.Ra6>

Pinning and pressurizing the bishop. Now if 36...Kc7 37.Bf3, and white will win back his piece with a material advantage and a winning attack.

<36...Qc7 37.Bf3!>

Black cannot save the piece via 37...Kd7, since 38.Ra7 pins and wins the queen (If 38...Bb7 39.Rxb7 again pinning ).

If black simply gives up the piece, white will win easily with his material advantage and crushing attack, but in any case,

<37...Bxf3>, trying to get two pieces for the rook, allows the white rooks to co-ordinate with the queen to finish the job.

<38.Rxd6+ Kc8 39.Qf5+ Kb8 40.Qxb5>

Opening the b-file for the e1 rook. Any move to the a-file leads to mate, whilst if now 40...Kc8 41.Qf5+ Kb8 42.Rb1 Bb7 43.Rd7 is completely devastating.

<40...Bb7 41.Rb1>

The d6 rook is immune since the black queen is tied to the defence of mate on b7. Black now cannot effectively prevent the threats of 42.Rd7 or 42.Rb6, followed by a cave-in at b7.

<41...Kc8>

Stepping out of the pin is the only chance, but after

<42.Qf5+ Kb8> back you go <43.Rdb6>

white will trade the two rooks for queen and knight on b7, and a get a materially winning endgame.

So finally, what happens in variation <C> <31...Rxd6>?

<31.Nd6+>, and now option <C> <31...Rxd6>

This one is much simpler.

<32.exd6>

If now 32...Kb6 33.Bf3 (threatening mate on b7), and any knight move allows 34.Qc5+ Ka6 35.Rxa5 Kxa5 36.Ra1#.

Or if 32...Kb8 33.Bf3, when knight moves are met by 34.Qa8#, or in the case of 33...Nxd6, 34.Qxd6+ Ka7 35.Rxa5#.

In either of these variations, black can give up the bishop to stop mate, but ends up with a materially lost position, eg, 32...Kb8 33.Bf3 Bc6 34.Qxc6 Qc8 .

But if black tries

<32...Nxe6>

amongst other winning lines is the simple

Move for move what I would have done.

Now I'm not claiming I saw all the way to the end from that first check with the bishop, but I played it out 'zactly the same (-:

To UdayanOwen:

It seems you were the only one here who recognized that after 31. Bd6+ Nd6: 32. d6:+ Rd6: 33. Qc5+ Rc6 34. Qa7+ Kd6 35. Qb8+ Rc7 there was the fine move 36. Qb6+ with # soon.

Congratulations!

I did not dig deep enough in the main line, because I simply concluded that after 31. Bd6+ Nd6: 32. d6:+ Rd6: 33. Qc5+ Bc6 the move 34. Ra5: would be easily winning. It was, in my opinion, at least necessary to see the defence 34. ... Qb8 and after that the fine 35. Qa3 (Should 35. Ra6 work, then this will also count, of course), which I would rate perhaps not as !!, but still easily as ! due to the beautiful underlying geometrical motifs.

Great solve by UdayanOwen (and by the others, too)!

Bye

I.2bb. 32. Ra5: (much more puzzle-like: That little finesse somewhere in the middle.)>

Please see my analysis on Pge 1 - It seems we are the only two analysts to investigate <32. Rxa5>.

Like you, I think it wins.

Omy gord it's right

brain score L0.50 R 0.50

Analysis by Fritz 11:

depth 21/42 time 4min30

1. (11.16): 31.Ba3-d6+ Nb7xd6 32.Qd5-c5+ Be8-c6 33.e5xd6+ Kc7-b7 34.d4-d5 Qg8-d8 35.d5xc6+ Ra6xc6 36.Qc5xb5+ Qd8-b6 37.Re1-b1 Qb6xb5 38.Rb1xb5+ Rc6-b6 39.Bg4-f3+ Kb7-c8 40.Rb5xb6 h6-h5 41.Ra1xa5 Kc8-d7 42.Ra5-a7+ Kd7-e6 43.d6-d7+ Ke6-f5 44.d7-d8Q

2. = (0.22): 31.Qd5-e4 Kc7-b8 32.Qe4-f5 Be8-c6 33.Bg4-h5 Qg8-d8 34.Qf5xf7 Bc6-e8 35.Qf7-f3 Be8-c6 36.Qf3-f6 Rh8-g8 37.Ra1-b1 Qd8-d5 38.f2-f3 b5-b4

Material: Down 2Ns for a B. The Black Kc7 is exposed to Qd5, Ba3, and Bg4, with Pd4 and Pe5 supporting the pieces. The Ra1 is ready to deflect Ra6 with the move Rxa5.

Candidates (31.): e6, Bd6+, Bf3

31.Bd6+

This is my best candidate, but the lines are so many, I cannot trace them in a reasonable time, so I suspect I am missing something.

One point from the computer analysis might add to the comments here. After

31. Bd6+ Nxd6 32. exd6+ Rxd6