1 axb6 ep #
Favorite puzzle. Mate in one!
That would be pretty easy if you were shown black's previous move, but without seeing b5 it certainly makes it more difficult :P
That's the essence of the puzzle. Saying axb6# is baseless without proof. I could have as well tricked you into 'mate in one'.
deathdream,
Sniperghost360's solution is the proof. Given the position, and that you stated it was white's move, with mate in one... It's stands to reason that, given the constraints/conditions of the puzzle, white's only way of getting mate in one is by capturing en passante. He could only capture en passante if black's last move had been ...b7 to b5; that that can only have been black's prior move and nothing else, is given, once again, by looking at the constraints of the puzzle. If that hadn't been black's last move, then white couldn't have made mate in one, and you wouldn't have presented this puzzle in the first place. Saying that it's possible that you're "tricking" everyone that it was mate in one is pointless.
Black's h-pawn is now on g6, the g-pawn on g7, the f-pawn on f7 and the e-pawn on f6. So the pawn on h3 must have started off as the Black d-pawn and could only have got there by d7-e6-f5-g4-h3, so h4-h3 was not Black's last move.
Also Ba7-b8 or b6-b5 could not have been Black's last move, because White would be in check. Also the e-pawn must have moved earlier to let the dark-squared bishop out, unless the dark squared bishop is a promoted piece.
So can the dark squared bishop be a promoted piece? Then which pawn was it? Well we already know Black has made 6 pawn captures with the d- through h- pawns. White has 9 units left on the board, so Black could have made at most one other capture. That means the b-pawn couldn't have promoted to a dark squared bishop, because it would have to make at least one capture and then the a- or c-pawn would also make a capture to end up on b5.
This is as far as I've got but I'm sure this is almost the full solution.
White to move and mate in one. There's actually a "rigorous" proof for 'that' i wonder if anyone of you can reason it out.