CEMC Cayley, 2006

Anne and Brenda play a game which begins with a pile of $n$ toothpicks. They alternate turns with Anne going first. On each player's turn, she must remove $1$, $3$ or $4$ toothpicks from the pile. The player who removes the last toothpick wins the game. For which of the following values of $n$ does Brenda have a winning strategy? (In a game, a player has a winning strategy if, regardless of what the other player does, there are moves that she can make which guarantee that she will win.)

(A) $31$ (B) $32$ (C) $33$ (D) $34$ (E) $35$