White to play and mate in 2.
Attribution: Glen Ferri
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asked Sep 26 at 11:12
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$\begingroup$ For a chess player, this is definitely [tactics] rather than [strategy] :) $\endgroup$– GlorfindelCommented Sep 28 at 11:50
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$\begingroup$ @Glorfindel There is no [tactics] tag here on Puzzling. $\endgroup$– Will.Octagon.GibsonCommented Sep 28 at 18:35
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$\begingroup$ Certainly; if there was, I would've edited it in. $\endgroup$– GlorfindelCommented Sep 29 at 16:09
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$\begingroup$ @Glorfindel If you feel it is appropriate, you could add a [tactics] tag to the set of available tags here on Puzzling and afterwards add it to my question. $\endgroup$– Will.Octagon.GibsonCommented Sep 29 at 19:33
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$\begingroup$ syzygy-tables.info/?fen=3k4/3B4/3K4/3n4/3B4/8/8/8_w_-_-_0_1 $\endgroup$– LucenapositionCommented Sep 30 at 6:01
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3 Answers
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The idea here is to force black to move their knight. We can see that the king is already in a state of not being able to move because of the white king and light-squared bishop. And we can see that the dark-squared bishop on any of these highlighted squares would be mate.
So all we have to do is bring the dark-squared bishop to f2 and so forcing the knight to move. The knight (moves highlighted in orange) cannot simultaneously block or defend bishop b6 or h4 mate at the same time, nor can it take the bishops or check the king to delay a mate in 2.
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The idea:
We notice that in the current position the Black King is pinned. We also notice that White could win in 1 move with Bishop D4-B6 or D4-F6, if only the Black Knight was not in D5, so defending both B6 and F6...
But, since, the Black King is pinned, if White could move so to force Black to move its Knight, i.e. while keeping the Black King pinned, and also keeping its own Bishop now in B4 ready to strike regardless of where the Black Knight gets moved...
The solution:
D4-F2: this is the only position where the White Bishop stays out of reach of the Black Knight but remains ready to strike;
D5-any allowed: Black is forced to move its Knight;
F2-B6 or, if the Black Knight is now in C7 or E3, F2-H4.
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$\begingroup$ Took me a minute to figure out why the bishop couldn't just move almost anywhere... I don't worry about stalemates enough. $\endgroup$ Commented Sep 29 at 11:18
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$\begingroup$ @JasonGoemaat If that's a hint, I don't get it. :) I don't see a risk of stalemate: the Black Night, as long as White does not capture it, can keep moving. Of course, that the Black Night cannot check in 1 or in any other way disrupt White's plan is a piece of the solution, anyway to me the strongest overall constraint is that White must mate in 2... $\endgroup$ Commented Sep 29 at 15:41
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$\begingroup$ Say bishop moves D4-E5 to force the knight to move. The knight can move to E7 to block the diagonal. If white then moves the bishop to F6 to pin the knight it's a stalemate, right? $\endgroup$ Commented Sep 29 at 19:56
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$\begingroup$ Yes, it is, but at that point the game of White mating in 2 moves in anyway lost, i.e. even if it wasn't a stalemate, so I don't think it is relevant to the present problem. $\endgroup$ Commented Sep 29 at 20:38
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1$\begingroup$ @JulioDiEgidio If black moves Nd6-e3, the alternate mate you give would also be mate. $\endgroup$ Commented Oct 11 at 19:58
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The black king can't move anywhere. So the black knight is forced to move. However, we can't move the black-squared bishop to f6 or b6 because it will be taken by the knight. The black-squared bishop must move to f2, such that if the knight goes to f6 to block the diagonal, the b6 square is open. One cannot move the black-squared bishop to h8 though, because the black knight can go to e7 and block the black diagonal. Therefore, black-squared bishop to f2 is the answer.
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$\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$ Commented Sep 29 at 19:27