I found 82. Bc8 and the winning lines thereafter!

<All> Wow! Somehow it feels there weren't too many kibitzers who came to provide an answer for this one (whether they knew the answer or not) - even for a weekend puzzle.

Oh well!

White to play (82.?) "Very Difficult"

This must have been the longest game from their Candidates match, which of course Fischer won 6-0. It's vaguely familiar, but I don't remember the winning procedure -- looks like a great study position though. Candidate moves are Kg5 and Bc8. At first I liked 82. Kg5, but rejected it because after 82...Nf7+ 83. Kg6 Ne5+ 84. Kf6 Kf4 85. Bc8 Nf3 followed by 86...Kg3 and it looks like a draw. But the other one should be winning.

82. Bc8! Kf4

At first I thought Black could play 82. Nf3, but then 82...Bb7+ Kf4 83. Bxf3 Kxf3 (or 83...Kg3 84. Bg4 Kh4 85. Kg6 Kg3 86. Kg5 wins) 84. Kg5 Kg3 85. h4 and the pawn queens.

83. h4! Nf3

Or 83...Ng4+ 84. Kg7 Kg3 85. h5 and the pawn will queen, by taking the knight if necessary.

84. h5 Ng5 85. Bf5 and Black is in zugzwang.

Much depends on what you consider "thinking" and, specifically, whether you consider memorization part of our "thinking faculty". Most people don't, reserving the use of "thinking" to (among other things) applying known principles to new situations. If we exclude memorization from our set of thinking tools, then we could not properly use memorized opening variations or endgame positions in games without also discarding our "thinking faculty".

And in this game it's just as much of a case of Taimanov missing the moves to draw (81...Nf3, 81...Kd4) than Fischer finding the move to win (82.Bc8). It's not necessarily fair to fault Taimanov since we don't know the time control situation, but by applying a little bit of "thought" Taimanov should have realized that the only way to draw was to either sacrifice his knight for Fischer's remaining pawn or to get his king to h8. Then combining both concepts by blocking the pawn's advance by 31...Nd3-f4 from where it could only be dislodged by capturing it with White's king, giving Black's king enough time to get to h8 via the dark squares, was really not that difficult to find. But given the state of the match at this point and possible time trouble, it apparently was too much for Taimanov. Not to take anything away from Fischer, he found the needed move when Taimanov didn't so he deserved to win. Perhaps this game is another validation of the saying that the winner of a chess game is the person who makes the next to last mistake.

BTW, also save the following link for future reference: http://chessok.com/?page_id=361. I think that it's somewhat easier to use than the other link to the 6-piece Nalimov tablebases and it usually provides the entire line for forced mate variations.

<And in this game it's just as much of a case of Taimanov missing the moves to draw (81...Nf3, 81...Kd4) than Fischer finding the move to win (82.Bc8)>

When I first saw this game it did look like Black had at least a few chances to draw the endgame. But I put it toward the weird game scheduling and Taimanov being more prone to fatigue.

If 81...Kd4 then Black's strategy is to either distract the White king by checks to allow the Black king to get to h8 via the dark squares white the White king is chasing and capturing the knight or to force White's king to the h-file where it blocks the h-pawn from queening. A possible continuation might be: 82.Be2 (or 82.Be1) 82...Ke4 83.h4 Kf4 84.h5 Nd7+ and now

(1) 85.Ke7 Kg5 86.Kxd7 Kh6 87.Ke7 Kh7 and the Black king can't be forced away from h8.

(2) 85.Kg7 Kg5 86.h6 Nf6 87.Bd1 (or 87.Be2 if 82.Bd1) 87...Ne8+ 88.Kh7 (otherwise the h-pawn is lost) 88...Nf6+ and a draw by repetition. If instead 87.Bb5 (or 87.Ba4 if 82.Bd1) to prevent 87...Ne8+, then 87...Nh5+ 88.Kh7 (again forced in order to protect the h-pawn) 88...Nf6+ and once again draw by repetition.