Impossible puzzle?

It does seem impossible. What did white capture on h3? The only missing black piece is the a8 rook, but it could not get out as the kings didn't move.

It does seem impossible. What did white capture on h3? The only missing black piece is the a8 rook, but it could not get out as the kings didn't move.
Okay, nevermind. The black rook could get out if the black b and c pawns played bxc6 and cxb6. That way there was an open file where the rook got out.
Does anyone know is this puzzle possible to solve?
The white pawn fell overboard. The kings did not move. Where should the pawn stand?
Is it mate in 1?
Does anyone know if this puzzle is possible to solve?
The white pawn fell overboard. The kings did not move. Where should the pawn stand?