A game of chess begins with 1.e4 (pawn to king four) and ends in the fifth move with knight takes rook mate. Reconstruct the game.
(One move in chess contains white's turn followed by black's turn.)
After deciding that it was impossible for White to win (I found no way for a white knight to get a black rook, and also giving check) I finally ended with the (wildly unlikely) following solution: 1. e4 Nf6, 2. Qe2 Nxe4, 3. f3 Ng3, 4. Qxe7+ Qxe7+, 5. Kf2 Nxh1#.
(In old style notation: 1. P-K4 N-KB3, 2. Q-K2 NxP, 3. P-KB3 N-N6, 4. QxP+ QxQ+, 5. K-KB2 NxR++)