White to move and win.  Difficult; probably impervious to engines.  Refer to the move list for pertinent variations.

good morning from good old germany

 

i play Be2 instead ... but it works also ;o) ...

the other ones are more difficult, i think

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If Be2, then Bd4+ or gxh2 is going to sting!

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Correct me if I'm wrong, but if Be2, then Bd4, Kg2. from here black is down a pawn and there's no real way to protect the g3 pawn since white has the h2 pawn that is protected by the king and the bishop is on the wrong square to provide coverage. Also if Be2, the gxh2 wouldn't you reach a similar end game with kxh2 or kxg2? Black once again is stuck unable to promote since the bishop is unable to provide coverage for both g1 and h2.

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Be2 loses outright.  The key is that black doesn't need to promote to win the game.  If white moves Be2 then 1...Bd4+ 2. Kxg2 Qxe2+ 3. Kxg3 Qe3+ 4. Kg4 Qe6+ 5. Kg3 Qxd6+ 6. Qxd6 Nxd6 and black is left with Knight and Bishop vs white's King and pawns.  It will be a difficult win for black but a win it will be.

It's essentially the same result the other way:
1... gxh2+ 2. Kxh2 Bd4 3. Kxg2 Qxe2+ 4. Kg3 Qe3+ 5. Kg4 Qe6+ 6. Kg3 Qxd6+ 7.Qxd6 Nxd6

not understanding the win for White in the final position : if Black sacs his Bishop for the h-pawn, then its rook pawn draw, right?

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No, white has a won game -

the Bishop guards the promotion square.  I'll demonstrate the win beginning from the point where the bishop is sacrificed for the promoted h-pawn. 

nice

Thanks Gonnosuke. I missed Qxe2. This was a great puzzle. Please post more.

Thanks for the post,
I only fail to see how 4.Bc4 is superior to Bd3, Be2 or even Bb5.

tricky

emmh

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 As was previously reviewed in post #5, Be2 and summarily Bd3 will loose out right to Bd4+. I'm not going to post the full line since it already has been posted. Bb5 is a waste of material as Kxb5 and white looses outright.

One of the things that makes this puzzle so difficult is the way that the 4 pawns in the g and h-files serve to misdirect.  It's like trying to solve a mathematical word problem with too much information in it.  Often times the hardest part of solving this sort of math problem is determining which information is actually useful. 

In the case of this puzzle, we're so used to factoring in pawns which are on the verge of promotion into our "endgame" thinking that it becomes easy to fixate on them and as a result we get lost in the weeds.

cool

Erm, why is this meant to be unsolveable for computers?