Very hard mate in 1

White's last move could be virtually everything and Bb2+ e7-e6...

@Sarg0n :
I see your Kubbel and raise an original.
lichess.org/editor/b4N1B/K4Qr1/R6b/4k3/qNp3pn/6R1/2QP3B/6Q1

For those who want real retrograde mate in 1, have at it. Karl Fabel and Werner Keym, 1967.
(Actual stipulation is "problem without words" - you aren't told that it's mate in 1, nor are you told the side to move, nor do you assume the side to move - you can logically deduce everything just from the placement of the pieces.)
lichess.org/editor/8/6P1/5QP1/5PPP/4BpPk/5P1p/4R2K/6BR

Think I solved it - I like "collinear" moves (here Q and R moving on the same line -or lane-).

Yep, you found the solution to the first. There aren't many ways to make a nonretro #1 difficult - add checks, add defences, and make the solution run counter to a chessplayer's subconscious instincts.

The second problem on the other hand is pure retro logic (no cheap tricks, everything is logically deducible) - if anyone wants a thoroughly-explained solution, do ask.

Nice puzzle, woulda been nice to see the previous move though.

There's no previous move, the position is blatantly illegal.

It's a good, but faulty problem as you can't prove enpesant is legal.

@Sarg0n thanks for making me feel like an idiot. :)
I thought for sure that I had it when I promoted my pawn to a knight...but, no, of course not. Very nice puzzle.

@Illion good ones, too. The second one was a bit easy, but the first one took me a few tries.

Oooh. It was only easy because e.p. was not flagged. Hmmmm.....