This particular mate in two managed to confound me for a couple of hours. I am sure if you give it a shot, you will soon see why!
White to move and win (Richard Reti, Kolnische Volkszeitung of 1928).
White to move and mate in 3 (A. Galitskiy, “Chess Journal”, 1900.) For added challenge, imagine that the players switch chairs (i.e. pawns moving in the opposite direction) and solve for mate in three again. Remarkable!