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Aug0710   JuliusCaesar: I spent ages on this puzzle, but just couldn't make Kg2 work – despite knowing it HAD to be the first move. 58. a6!!! completely eluded me. To be fair to myself, I always try to solve these puzzles without setting the position up on a board. But this one was just far too hard. The skill and vision of these top GMs is simply amazing. 

Aug0710
  Once: <jahhaj> You are, of course, quite right. I was counting on the fact that the black king couldn't get to a1 because he will be on the wrong side of the pawn. But the white king is one square too far away for that to work. Safer to leave black's useless b pawn on the board as it prevents any sneaky stalemate traps. 

Aug0710   ounos: click for larger view
<Once: Black has been forced to put his king on c1, blocking the c2 passer. This means that white has a free move. He could grab the b pawn or he could play Kg2. Repeat until won by white.>
If he grabs the b pawn, it's a draw, since next time there is Kb1 and Qb3+ check, the answer is Ka1, not Kc1. So white should aim for two such "extra" moves to get his king closer, to bring a position like this:
click for larger view
Where it would finish 1. ...Qxb4 2. Kd1 Qe1# 

Aug0710   4tmac: Liked this one. Note that Once's first diagram is a draw without the b Pawn. A problem would have something like this where QxP wins click for larger view 

Aug0710
  OhioChessFan: 58 or 59. a6 is the key move in the position. Easy for a GM to see, a bit tougher for us patzers. 

Aug0710   nuwanda:
thats the sort of puzzle i like most...
as for most here it was immideatly "clear" that 55.Kg2 is whites only try. after 55...Kxe4 56.c5 bc 57. b5 Kd5 you find the solution 58.a6 easier if you know the game Capablanca  Ed. Lasker from a simul 1913 in London (or you have studied your Dvoretsky well which may be the same)
click for larger view
in this position Lasker spoiled the draw (which he could have reached by 1...Ke6) by playing 1...Ke5 2.h6 10 so instead of 57...Kd5 the race has to be considered
57...c4 58.b6 ab 59.a6 c3 60.a7 c2 61.a8Q+ Kd3 ending in the following
click for larger view
i am a little surprised that most people here considered this an easy win as black, due to his b6pawn, cannot use the usual stalemate. But on the other hand the white king first has to take the h2pawn and then come over to the queenside which gives black some extra time. in my calculations it was not clear to me whether this is enough for white. it turns out to be won but if the black pawn was e.g. on b5 instead of b6 it would be a draw as a look in the tablebases will tell you. play might continue 62.Qa1 Kd2 63.Qd4+ Ke2 64.Qc3 Kd1 65.Qd3+ Kc1 66.Kxh2 b5 67.Kg2 b4 and here white has to find the only winning move 68.Qb3 Kd2 69.Qb2 Kd1 70.Kf2 10 instructive... 

Aug0710
  Once: Ah, the old queen vs king and bishop pawn stalemate trap. It feels like an old friend that we have discussed more than once before  if you will forgive the pun. Here's the theory, courtesy of Muller and Lamprecht's Fundamental Chess Endings: click for larger viewThis position, with white to move is a draw, because black can hide his king on a1 when Qxc2 is stalemate. For white to win this, his king needs to be inside this zone: click for larger viewIf the white king is on one of the squares denoted by a white king or inside, then he wins by creating mating threats with his king and queen working together. For example, he may be able to play Ka3 and Qa2# while black is snucking his king into a1. White also gets mating threats on the wrong side of the c pawn eg. black king on d1 and a protected white queen on e1. When the black king is on the other side of the bishop pawn, the winning zone is quite a bit larger because it takes black longer to get to a1. click for larger viewWhite wins if his king is inside this zone and with best play it's a stalemate otherwise. In other words, it's okay for white to play Qxb6 during one of the cycles where he has forced the black king to c1, but not the first cycle as the white king is too far away on h1 or h2. But easiest of all is to play Kg1 or Kg2 and leave the b6 pawn alone. 

Aug0710
  paulalbert: Being a sub 1500 rated player,I thought this was relatively easy for Saturday. Clear that offering the sacrifice of the N by Kg2 and then pushing c5 the only winning chance as opposed to bringing N back to stop h pawn. Have to see the nuanced variations of course that assure black K can't get back into the square to stop white from promoting. Very instructive.
Too me the variation after Kd5, c6 as played seemed like an elementary win. I was surprised that Akopian played Kd5. Paul Albert 

Aug0710
  agb2002: White is a knight up.
Black threatens 55... h1=Q+ and 55... Kd4 to capture the white pawns. These threats and the pawn majority suggest 55.Kg2, keeping the knight close to the pawns: A) 55... Kxe4 56.c5
A.1) 56... Kd5 57.c6 followed by Kxh2 with a won pawn ending. A.2) 56... bxc5 57.a5
A.2.a) 57... c4 58.b6
A.2.a.i) 58... axb6 59.a6 c3 60.a7 c2 61.a8=Q+ and the pawn on b6 does not allow the stalemate defense with the black king on a1. A.2.a.ii) 58... a6 59.b7 c3 60.b8=Q c2 61.Qb2 Kd3 62.Qc1 + . A.2.a.iii) 58... c3 59.bxa7 c2 60.a8=Q+ Kd3 61.Qc8 Kd2 62.Qxc2+ Kxc2 63.a6 + . A.2.b) 57... Kd5 58.a6
A.2.b.i) 58... Kd6 59.b6 axb6 60.a7 + .
A.2.b.ii) 58... c4 59.b6 Kc6 60.bxa7 + .
B) 55... Kd4 56.c5 bxc5 57.a5 with similar lines. 

Aug0710
  kevin86: Funny,the key required white to give up the knight! 

Aug0710   eightsquare: Surprisingly easy for a Saturday . got it. 

Aug0710
  Marmot PFL: Luckily I tried 55 Kg2 1st, or it would have taken longer. 55...Kxe4 (55...Kd4 56 Nd2 or 56 c5 anyway) 56 c5 bc (56...Kd5 57 c6 wins as there is no stalemate) 57 a5 Kd5 58 a6 (not 58 b6 Kc6) and b6 wins. If 57...c4 58 b6 ab 59 a6 (not b6, must queen with check). 

Aug0710
  Jimfromprovidence: FWIW, what helped me understand the concept of opposition in this case was by simplifying the text after 58 Kxh2. I had no idea that the position at this point was a win for white. click for larger viewSo I played 58...a6, seeing 59 Kg3 (not bxa6) 59...axb5 60 axb5. click for larger viewThen I plugged the position into the Nalimov tabebases and followed along. 

Aug0710
  Eggman: Got this pretty quickly, I must say. Pretty, though. <<TacticalMonster: In the game continuation, I found a pretty interesting variation. One way to continue:
55 Kxe4 56 c5 Kd5 57 c6 Kd6 58 Kxh2 a6! (trading pawns in defensive position is good technique) 59 Kg3 axb5 60 axb5 Kc7 61 Kf4 Kd6 62 Kf5 Kc7 63 Ke6 Kc8 64 c7! (the key move! any other move draws) Kxc7 65 Ke7 Kc8 66 Kd6 Kb7 67 Kd7 Kb8 68 Kc6 Ka7 69 Kc7 Ka8 70 Kxb6 with basic winning king and pawn ending>> There's one more thing to be said at the end here: on 70...Kb8 White should play 71.Ka6!, since the natural 71.Kc6?! is met with 71...Ka7! and White has nothing better than 72.Kc7 (72.b6+?? Ka8! =) Ka8 73.Kb6 Kb8 and it's deja vous all over again. By the way, when giving a move by Black, such as Black's 55th move 'Kxe4', the proper format is "55...Kxe4", with the '...' indicating that it is Black's turn. 

Aug0710
  TheBish: Shirov vs Akopian, 1992 White to play (55.?) "Very Difficult"
The tendency here would be to stop Black's pawn from queening with the knight... which doesn't work! After 55. Nf2 (or Ng3) Kd4, White will manage only to draw, i.e. 56. Kg3 Kxc4 57. Kxh2 Kb4 58. Ne4 Kxa4 59. Nd6 Kb4 60. Nc8 Kxb5 61. Nxa7+, etc. The key is to give up the knight, and see that the resulting K+P endgame is winning, by one tempo, as White will queen with check! 55. Kg2! Kxe4 56. c5! bxc5
Otherwise 57. c6 will be very simple.
57. a5 c4 58. b6 axb6 59. a6! h1=Q+ 60. Kxh1 c3 61. a7 c2 62. a8=Q+ Kd3 63. Qd5+ Kc3 64. Qe5+ Kb3 65. Qe3+ Kb2 66. Qd4+ Kb1 67. Qb4+ Ka2 68. Kc3 Kb1 69. Qb3+ Kc1 70. Kg2 and White will continue in similar fashion, forcing Black to blockade his c2 pawn with ...Kc1, gaining time to bring his king closer for the final mating attack. Black's extra bpawn here prevents the normal drawing technique of Black moving his king to a1, which would result in stalemate after Qxc2 and not allow White to inch his king closer. 

Aug0710
  Peligroso Patzer: It is rather surprising that a strong GM such as Akopian would play <56. … Kd5?>, which obviously loses. At that point, Black’s best try would have been <56. … bxc5>, which is still theoretically losing, viz., 57.a5 c4 58.b6 axb6 59.a6! [only move] (For example, if 59.axb6? c3 60.b7 c2 61.b8=Q c1=Q 62.Kxh2=) 59. ... c3 60.a7 c2 61.a8=Q+ Kd3 (or 61...Ke3 62.Qh8 (But NOT 62.Qd5?? h1=Q+ 63.Kxh1 c1=Q+ 64.Kg2 Qd2+ –+) 62...Kd2 63.Qd4+ Ke2 64.Qc3 Kd1 65.Qd3+ Kc1 66.Kxh2 Kb2 67.Qd2 Kb1 68.Qb4+ Ka1 69.Qc3+ Kb1 70.Qb3+ Kc1 71.Kg2 Kd2 72.Qb2 Kd3 (72...Kd1 73.Kf2 Kd2 74.Qd4+ Kc1 75.Qb4 b5 76.Ke3 Kd1 77.Qd2#) ) 62.Qa1 Kd2 63.Qd4+ Ke2 64.Qc3 Kd1 65.Qd3+ Kc1 66.Kxh2 Kb2 67.Qd2 Kb1 68.Qb4+ Ka1 69.Qc3+ Kb1 70.Qb3+ Kc1 71.Kg2 b5 72.Kf2 Kd2 73.Qd5+ Kc1 74.Qxb5 Kd2 75.Qd5+ Kc3 76.Qe5+ Kd2 (or 76...Kb3 77.Qa1 ) 77.Qe3+ Kd1 78.Qe1#. 

Aug0710
  Peligroso Patzer: BTW, to supplement the analysis in my previous post, in the following position (<after the hypothetical 56. ... bxc5 (in lieu of Akopian's actual 56. ... Kd5?) 57. a5>: click for larger viewIf Black tries <57. ... Kd5>, then White wins with <58.a6!> (But NOT 58.b6?? allowing Black to win with 58. ... axb6 59.a6 (or 59.axb6 Kc6 60.Kxh2 c4–+) 59...Kc6–+) <58...c4 59.b6 axb6> (or 59...Kc6 60.bxa7 ) <60.a7 >. 

Aug0710
  Peligroso Patzer: One other feature of this endgame that I find fascinating is that in the following hypothetical position:
click for larger view
… which could have arisen if Akopian had played <56. … bxc5>, and play had then continued: <57. a5 c4 58. b6 axb6 59. a6 c3 60. a7 c2 61. a8=Q+ (See diagram.)>, White’s main winning idea is 62. Qa1 to control the promotion squares of both Black’s c and hpawns (for example 61. ... Kd3 62. Qa1 ); however, if Black (from the diagrammed position) plays 61. … Ke3, then White can also win by playing the Queen to the opposite corner, 62. Qh8, since 62. … c1=Q allows the skewer, 63. Qh6+, and if Black desperately tries the diversion, 62. … h1=Q, then White simply takes with the Queen, 63. Qxh1 (but NOT 63. Kxh1??, allowing promotion with check, 63. … c1=Q+, when White has no time to play the skewer, and the resulting position is actually a tablebase win for BLACK). 

Aug0710   messachess: This was not difficult at all. I usually do not get them immediately like this time. But, I was figuring on 56...bxc5. This problem lends itself to intuitive solutions. One way (as in game) or another (b takes), it's either, black cannot catch the pawns, or, as in the game, it's a Zugzwang. 

Aug0710   ZUGZWANG67: Pawns are equal but W has a N. B has an easily stopable passed Rp on the 7th rank while W has a 3 vs 2 majority on the Qside. Those 2 last considerations will dictate the final outcome: everything is settled for a pawn race obtained by means of a breakthrough. W's first order of business is to put the threat at h2 under control. But how? By bringing the K or the N? The N, of course, if we're planning to break by c5: B must be obliged to capture with his bpawn and not the K. So the WK shall come to h2, sacrificing the N in the process. But after c5 and bxc5, who promotes first? Both promotes on the same move, since from c5 B needs 4 moves to do the job while W needs 4 moves as well, that is: a5b6bxa7a8Q. The fact that B could interpose ...axb6 after b6 is irrelevant here, as he loses the one move that W uses for recapturing: 51=4. In the same manner, ...h1Q+ amounts to nothing. At the end, it's the fact that W promotes with check at b8 that decides, since he is the one who plays the first of the 4 requested moves. In terms of notation of moves, I think we should see something like 55.Kg2! Kxd4 (otherwise the N will capture the eventual B's passed pawn when this latter comes to c3) 56.c5 bxc5 57.a5 c4 58.b6 c3 (58...axb6 59.a6! (not 59.axb6? c3 60.b7 c2 61.b8Q c1Q is draw: promoting at the same without check is not enough for a win) 59...c3 60.a7 c2 61.a8Q+; 58...a6 lets W promote first: 59.b7 c3 60.b8Q c2 61.Qc8) 59.bxa7 c2 (59...h1Q+ 60.Kxh1 c2 61.a8Q+) 60.a8Q+ Ksafe 61.Qc8. A nice one. Time to check if my delirium is just imaginary. XD 
Hm. Interesting. I don't think this puts my analysis out of business, since the fact that W has the opposition is unimportant here. Let's suppose that W is on move here after 60.Kf4 and so, B has the opposition: click for larger viewThe BK is restrained in its mobility: it must watch for the c7 push. Furthermore at some point B is likely to lose the opposition since the d7square is out of reach. So 61.Kf5! Kc7 (61...Kd5 62.c7; 61...Ke7 62.Ke5) 62.Ke5 Kc8 (62...Kd8 63.Kd6) 63.Ke6 Kd8 (63...Kb8 64.Kd7) 64.Kd6 Kc8 65.c7 Kb7 66.Kd7 Ka8 67.c8Q+ is mate. click for larger viewOverall I believe that the general theme of that puzzle (the one published by CG) is one of deciding which piece to be used by W to deal with the h2pawn. 

Aug0710   ZUGZWANG67: <Peligroso Patzer: <It is rather surprising that a strong GM such as Akopian would play <56. … Kd5?>, which obviously loses.>> I'm wondering whether the time will come when, instead of always questionning why a certain GM played this or that, we will start promoting time controls that allow players time for thinking about what they play during endgames... :) Peace! 

Aug0710
  OBIT: <Zugzwang>From your first diagram, after 61. Kf5 I think Black's best try is 61...a6, which leads to 62. Kf6 (62. ba?? Kxc6 draws) Kc7 63. Ke6 ab 64. ab Kc8. This is a position mentioned by <tacticalmonster> about a page back, which is won by 65. c7! Kxc7 66. Ke7 Kc8 67. Kd6 Kb7 68. Kd7 Kb8 69. Kc6 Ka7 70. Kc7 Ka8 71. Kxb6. By the way, I'm guessing this was the wishing thinking in Akopian's head when he played 56...Kd5, allowing 57. c6. He saw 56...bc was going to lose to a6!, then suddenly remembered there are stalemates in some of these positions where the king gets to the corner. A short time later, he remembered the c7! trick and realized the stalemate try wasn't going to work, so he resigned. Since we never got to see c7, his play ends up looking a little silly. Sometimes GMs should play a few moves longer, just to let the public know what is really going on. 

Aug0710
  Jimfromprovidence: <OBIT> <This is a position mentioned by <tacticalmonster> about a page back, which is won by 65. c7! Kxc7 66. Ke7 Kc8 67. Kd6 Kb7 68. Kd7 Kb8 69. Kc6 Ka7 70. Kc7 Ka8 71. Kxb6.> <tacticalmonster> <In the game continuation, I found a pretty interesting variation. One way to continue: 55 Kxe4 56 c5 Kd5 57 c6 Kd6 58 Kxh2 a6! (trading pawns in defensive position is good technique) 59 Kg3 axb5 60 axb5 Kc7 61 Kf4 Kd6 62 Kf5 Kc7 63 Ke6 Kc8 64 c7! (the key move! any other move draws) 64…Kxc7 65 Ke7 Kc8 66 Kd6 Kb7 67 Kd7 Kb8 68 Kc6 Ka7 69 Kc7 Ka8 70 Kxb6 with basic winning king and pawn ending> This is just a small point of order for the record, but the line posted by <tacticalmonster> you reference in your post needs some clarification. After move 63 by black, here is the position.
click for larger viewAt this point, any move by white wins in this position (not c7 only). However, c7 , sacrificing the pawn, does need to be played at some point for black to win. Below is the position after 70 Kxb6 in his diagram which proves his point.
click for larger viewSo, only those who saw this "trick" solved the puzzle fully. 

Aug0710   tacticalmonster: <Jimfromprovidence> On move 64, you are right about the fact White can play any move and still wins but 64 c7! is the quickest way to victory. White can play 64 Kd6, Kd7 or even Kd5 but eventually all those moves would tranpose back to c7!. This pawn sac is simply the key to winning this ending. 

Aug0710
  Jimfromprovidence: <tacticalmonster> <This pawn sac is simply the key to winning this ending.> Yes, we are in total agreement.
You figured out the correct line if pawns are traded and <OBIT> summarized the overall position at move 56 nicely. I knew this puzzle was not that easy after 58 Kxh2. 



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