Xjyuk

Lots of pieces are tangled here.

Can you find mate in one?

There certainly is more than meets the eye here.

First of all,

It cannot be white's turn: if it were, black's previous move would have been either knight takes (knight or rook) on b4 OR d-pawn takes on c1 and promotes to queen: any other move would have been made from an illegal position. In particular, the knight cannot have moved to an empty b4, because then the white bishop would have been checking the black king on white's previous move, which is illegal. In case you were wondering whether the white bishop could have captured something on c3 to give check legally, that's also impossible, since a black pawn would have needed to capture to get there, and the rest of the black pieces are still on board. But could there have been a promoted black piece there? HMMM.. Looks like this needs another chapter, because the captures made by the white pawns aren't quite trivial.

EDITED: dig down the rabbit hole to see how far it goes:

If there was a promoted black piece on c3, let's see which pawn it was. Black's a, b, and c-pawns are still on the board, so it wasn't any of them. White's b-pawn must have taken a promoted piece on the c-file, and black's d-pawn (or another promoted piece) to get to the d-file. White's h-pawn must have been promoted to replace the piece captured on the b-file. For this to happen, it must have captured black's g-pawn, or another promoted piece. White's g-pawn has also taken at f3.

So we can account for

3 black pawns on the board, d and f black pawns taken, black g pawn promoted to replace the piece white's h-pawn took, and the black h-pawn promoted and then fed to white's b-pawn on c-file. This leaves black's e-pawn. Could it somehow have gotten promoted? Or could it have sacrificed itself to clear a promotion path for another pawn? Not without some additional black pieces taken, it seems, so it must have died a meaningless death.


All this means that there couldn't have been many enough promoted black pieces in the game in order for one of them to have been at c3.

Back to the business, since the rabbit hole seems to have checked out:

Now then, both of the two moves suggested (in bold) in the first spoiler block are also impossible, because they'd need to capture a piece. Because black has a doubled pawn, one white piece was necessarily taken earlier, and white has the rest of the pieces still on the board.


Since black has no legal last move, it must be black's turn.

Now that we have that established, we need to figure out

what could have been white's previous move. This is tricky, since black still has very few options to account for a legal previous move.


Any move "on the outside" leaves black without a legal previous move, and as long as the white pawn at d4 was still there, the c3 bishop must have been on the black king's diagonal, meaning that the black knight couldn't have moved either. Therefore, the previous black piece to move would have been either the queen or the pawn at b5. Since there aren't any squares the queen could have come from (even allowing for one white move afterwards), and the pawn move also proves impossible (there's no way the white rook could legally have gotten to c5 in that case) we must deduce that white's d4 pawn cannot have been there two moves ago, because black's previous move must have been with the knight, and so the white bishop cannot have been on the black king's diagonal.

Now this is interesting, because it means the pawn was somewhere else. If it were on d3, the black knight would have nowhere to have come from,

so white's pawn was on d2, black's knight was on d3, and white's bishop was somewhere else, like e5, for example.

So three half-moves ago, the board must necessarily have looked something like this:

(white's dark square bishop could also be elsewhere on the long diagonal)

From which the only way to reach the current position is

1. Bc3+ - Nb4
2. d4

Which finally allows for the long sought after mate in one:

2. - cxd3 e.p.#!

I may have missed some specific variations, please drop a comment if you notice one. And thanks again, OP, for another brilliant puzzle!

Nxc4

is mate because

pawn b5 is pinned

To add on to Glorfindel's answer,

...cxd3 is also mate, assuming white just played d2 to d4. The question doesn't state if we're finding mate for white or black.