Here is another mate-in-one of my own i.e. a not quite usual one...
[title "Mate in one"]
[FEN "3b4/R3P3/2kPR1n1/P1p1n3/4K1p1/2Nr4/5p2/1b6 w KQkq - 0 1"]
Imagine, you walk into a chess club, an abandoned chessboard hangs out on a table. You take a look at the position. You don't know where white or black is, who to play, yet one thing is certain: there is checkmate in one move...
There are two checkmates per orientation:
[title "Mate in one"]
[FEN "3b4/R3P3/2kPR1n1/P1p1n3/4K1p1/2Nr4/5p2/1b6 w KQkq - 0 1"]
1. exd8=N#
and
[title "Mate in one"]
[FEN "3b4/R3P3/2kPR1n1/P1p1n3/4K1p1/2Nr4/5p2/1b6 b KQkq - 0 1"]
1... Rxc3#
and
[title "Mate in one"]
[FEN "6b1/2p5/4rN2/1p1K4/3n1p1P/1n1RPk2/3P3R/4b3 b KQkq - 0 1"]
1...c6#
and
[title "Mate in one"]
[FEN "6b1/2p5/4rN2/1p1K4/3n1p1P/1n1RPk2/3P3R/4b3 w KQkq - 0 1"]
1. e4#
It looks like
e7xd8=N (by White)
is checkmate, but so is
Rd3xc3 (by Black)
So perhaps there's more to this puzzle than meets the eye ...
That's a nice archaeological find. However, I'm not so sure there is in fact a checkmate in just one "move". Of course, there is a (unique!) checkmate for both colors in all orientations considered by @Brian Towers, which makes this a very nice problem indeed. But what about the other orientations?
You may protest that there's a rule that the bottom right corner must be a light square, but I think you're going to have to consult a historian to determine whether this rule was in effect in this particular late 19th century London chess club, and in particular whether the game could have continued without rotating the board if the players noticed their error during the game. You likely also need to consult a medium in order to determine whether one of the players noticed it. So, I think this rule doesn't mean we can exclude other orientations.
You may argue that the other orientations are excluded because there's a pawn on the side of the board. Not quite. First, a pawn can never legally be put on the first rank, so that excludes one orientation (white being to the left of our current view). But this is not true for the eighth rank. Promotion of a pawn is done by first moving the pawn to the promotion square on the eighth rank, and then replacing it with another piece. So, it is possible for a pawn to be on the eighth rank in a legal game. Of course, in the current state of the board the move is not yet completed, but that doesn't matter. We already know that in the other orientations the game was ended before the checkmate (as we still have to make one move), so the same could happen in the middle of the promotion move. I certainly have seen the board being left abandoned in such a state at my own chess club.
It could be possible that we can show the position is unreachable via retrograde analysis, but that seems very difficult, so I'm just going to leave that to others and just say that I don't know how to prove this one way or the other.
Ok. So, let's assume the pawn on the side from our orientation is mid-promotion. Now suppose white wanted to promote into a knight. This is check, but not checkmate, as black can take the knight with the bishop. However, black cannot give mate here while getting out of check at the same time. So, neither player can give checkmate in one move. (technically, I have shown this is not possible in one half-move, but I believe the technical term "Mate in one" is generally understood to refer to one half-move)
In conclusion, I believe I have made a decent argument for why there exists a scenario where this position has been reached from a perfectly legal game (under the rules in this particular chess club), yet there exists no mate in one. Hence, however unlikely my scenario may be, I must conclude that I cannot be certain that there is checkmate in one move.
That said, I don't think my problem hurts the essence of your archaeological find clever composition. As long as the promoted piece can deliver checkmate as well, we can be certain that there is a mate within one move.
I think just placing a pawn between the bishop and the pedantic promotion square would do:
[title "Mate in one"]
[FEN "3b4/R3P3/1pkPR1n1/P1p1n3/4K1p1/2Nr4/5p2/1b6 w - - 0 1"]
I believe this does not change the checkmate moves in the other orientations, or even their uniqueness. It does make the checkmate for white easier to find in the other orientations, but I think the new orientation you get in return is more than worth it. Maybe there are retrograde arguments against this position, I'm not sure.
If we assume that the players were not bad at chess, then the move before this move, that player had to have something more important to do than checkmate their opponent.
If we take the board orientation as black moving upwards, with the white king at e5 and black rook at (e.g.) a6, then black moves rook to e6, check, white moves king to d5, black moves pawn to c6, mate.
If it was white's turn, for either orientation, there is no move that black would have made on the previous turn besides checkmate. Likewise if black is moving down, white would have mated black on the previous turn.
I think the only solution is black moving up, pawn to c6.
Looks more like black plays rd4++ and mates white.
