Question 95
Two players play the following card game. They have a deck of $n$ cards. For every two cards it is known which one of them takes the other (it may happen that $A$ takes $B$, $B$ takes $C$, and $C$ takes $A$). Initially the deck is distributed between the players in an arbitrary way. On each move, the players open the topmost cards of their decks; then the player whose card takes the opponent's one gets both cards and puts them to the very bottom of his deck (in an arbitrary order). Prove that for any starting situation, the players may agree to play in such a way that one of them will finally get an empty deck. (E. Lakshtanov)