The following position appears as the 7th puzzle of Raymond Smullyan's Arabian Knights, a book of retrograde analysis:
[fen "3qk2r/p2pp1bp/bpp2n2/8/3N3Q/1PN1P1P1/P1PPP2P/3K1n2 w - - 0 50"]
The conditions given are "both [White's] castles [=rooks] captured on the same row, Black queen's castle [rook] captured by a pawn, and king's bishop given as odds." The stipulation is that you must find where White's castles [rooks] were captured.
I puzzled over this for quite some time, then gave up. Very early in the solution, it is stated that "Since the Black king has not moved, ..." However, I do not see how this can be inferred from the position. Is it necessarily true? Couldn't the Black king and queen have moved out of the way of the Black rook (which was captured on e3), then moved back? I do not see "non-movement of the Black king" among the conditions, or anything about Black being able to castle.