'A game begins 1 e4, and ends on move 5, with the move, knight takes rook. What was the game?'

"This is the famous 1999 ChessBase Christmas puzzle. Frederic Friedel tells a very amusing story about it. This happened in 1986, when he was travelling by car, from Zurich to Lucerne, in the company of Karpov and Kasparov, the two best players in the world. To entertain them, during the journey, he set them this problem. They tried to find the solution during the whole journey, and during the following days in their hotel: with no success.

One day -- a goodly time later -- Frederic Friedel found on his answering machine, a message from Kasparov, with the urgent request to ring him back. Friedel rang back, and came upon a noticeably disgruntled Kasparov: "You are a dead man, Fred. You have put me in a very embarassing situation."

"What had happened? He, Kasparov, had together with Botvinnik, set this problem to the students of the latter's chess school, and gave them some days to think about it. When the students got nowhere, and asked for the solution, the thinking time was extended by a day, during which Kasparov and Botvinnik also worked intensively on the problem. Kasparov was even of the opinion that the problem had been wrongly set, and was impossible to solve. This is how it came to his call to Friedel. When the latter gave the solution over the phone, he could clearly hear Botvinnik in the background, groaning in surprise."

"Many years later, Frederic Friedel set the problem again, as the ChessBase Christmas puzzle."

From chessproblem.net

1 e4 Nf6 2 Qe2 Nxe4 3 f3 Ng3 4 Qxe7+ Qxe7+ 5 Kf2 Nxh1#