Failed study by F. Hey, 1913, which is example 272 in Test Your Endgame Ability by August Livshits and Jonathan Speelman (1988) which followed the composer's incorrect claim that White to play could force a win. There are many traps but a defence is possible.
In Averbakh's Comprehensive Chess Endings, volume 2 (example 238, pages 89-90) the correct result is found by a method of corresponding squares.
The composer's task was White to play wins, Black to play draws. The latter is correct (1...Bd6), as in the Speelman book, but the tablebase agrees with Averbakh that Black can also draw when it is White to move. Some of the variations are instructive.
F. Hey, 1913 - Refuted by Averbakh
is the supposed solution in the book. Obviously White wants to play Nf7 mate in two and threatens to do this via either d8 or g5. Black must manoeuvre his B to prevent this. [1.Nc6
also threatens Nd8 with Ne5 as the alternative route if Black covers d8. 1...Bc7
and both routes are defended. (1...Bh4?
) ] 1...Bh4!=
Prevents the mates. White can try to combine threats to the a-pawn with mate threats but Black can cope: [1...Bc7
and mates (NOT 2.Nxc7
stalemate: the "point" of the study.) ] 2.Ng7!?
is one way to head for c4, the only other square from which the a-pawn can be threatened. This is not as dangerous because from c4 White is only in contact with e5, not with d8. Black has three possible replies but they require precise follow-up. [2.Nd4
to approach the a-pawn via c6, which is in contact with both d8 and a5. 2...Bg3!
This correspondence (Nd4/Bg3) is missing from Averbakh's explanation. 3.Nf3!
Tests Black from another direction. From here the knight can reach c4 (via d2), c6 (via d4 or e5) or f7 (via e5 or g5) in two moves. Averbakh says that only one square for the bishop prevents all these tries and so corresponds to f3: (3.Nc6
3 Nb3 transposes to the note to move 3 in the main line. 3...Bc7
This is the same as the 1 Nc6 line.) 3...Bf4!
This cuts out d2, e5 and g5, leaving only 4.Nd4
which we have already noted is answered by 4...Bg3
repeating the position.; 2.Nc5
Idea Nb7, so that the N heads for the d8-f7 route while also attacking the a-pawn. 2...Bg3!
Trying from the other direction but there are two replies that hold: 3...Bc7
) ) 3...Bc7!
The most amusing, but 1...Be7 or 1...Bg3 would be more practical. 3.Nf5
White ignores the bishop and continues the agenda. (3.Kxg5
Black blocks both routes to c4 (d6 and e3).; 2...Be7
) ] 3.Nf5
heading for c4 via d6 or e3 3...Bf4
Black prevents both those moves. 4.Ne7
Now any square on the b8-h2 diagonal (to meet Nc6 by Bc7) is safe, except for 4...Bc7??
when White wins by zugzwang [4...Bg3
draws, for example, if 5.Kh6
attempting the only other winning manoeuvre (Ng6 mate), Black simply plays 5...Bf4+
repeating the position.] 5.Nc6
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