[ Game Theory_(miscellaneous) ] [Evenness and Oddness $]

Under the Christmas tree, there are 2012 cones. Winnie-the-Pooh and donkey Eeyore are playing a game: they take cones for themselves in turns. On his turn, Winnie-the-Pooh takes one or four cones, and Eeyore takes one or three. Pooh goes first. The player who cannot make a move loses. Which of the players can guarantee a win, regardless of how the opponent plays?
First, Winnie can take four cones, and then take one cone each time afterwards. In this case, after each of Eeyore's moves, there will be an odd number of cones left under the tree. As the number of cones under the tree gradually decreases, inevitably, there will come a moment when only one cone is left under the tree. By taking it, Winnie will win.

## Answer

Winnie-the-Pooh.