2006 Cayley Problem 24

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.)

\textbf{(A)}\ 31\quad \textbf{(B)}\ 32\quad \textbf{(C)}\ 33\quad \textbf{(D)}\ 34\quad \textbf{(E)}\ 35

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.