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Lovely puzzle from my game

After black moves 43...Nb2, what is white's best move? Playing white I missed it. Hint: forget about advancing the pawn, or capturing pieces.

Ok, another hint: mate in 3. Still hard. No takers?
A cute idea. But since d6 wins without a hitch anyway, not too crucial.
Yes, that was pretty hard for me. For me the way I solved it was to realize what square you need to close off, and then realize it can't be done via conventional means. But I dont spot this if not told it was a puzzle, and it would probably give me problems in puzzle storm.
@MrPushwood

True, but of course the other pieces on the board could have been different, where the mate would have been the only way to win. It's always good to see these things; you never know when you'll need them.

@ArtNJ

Yeah, as one can see, I missed it too. It's counterintuitive because first you have to sac the bishop to get nothing in return, then it's still two more moves to mate. Plus you have to notice that the K has to take the B or else it's mate in 1.
@Zubbubu
At first instinct I thought for Bh6 because for a player like me it's quite natural to play Bh6 because of logical continuation 45. Rf5# and then I found it: Kxh6 Rg7 (stopping any possible flight squares) any move g4#
If I have not missed something, then it looks cool checkmate!
@Akbar2thegreat

Yes, there are several things one has to notice, and in a rapid game one will just go for the obvious win of d6. But I suppose a very advanced player would see it.
@Zubbubu
Most likely I wouldn't have found it in a Blitz game of 3+0, but in any slow time control from 8+0, I would have found it.
@Akbar2thegreat

Well I missed it in a rapid 10/1. But as @MrPushwood said, the more obvious if longer win was simply d6, so I wasn't looking for the mate.

In general, the hardest sacs to notice are these sorts, where you don't even capture a pawn, but simply displace a piece to set it up for the kill, in this case the K. I've seen a puzzle where you set up a queen for a KQ N fork by throwing away a piece that the Q has to take. I wish one could have a data base of just these puzzles, to overcome the counterintuitive feel to these positional sacs.

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