2006 Pascal Problem 24

A bag contains eight yellow marbles, seven red marbles, and five black marbles. Without looking in the bag, Igor removes N marbles all at once. If he is to be sure that, no matter which choice of N marbles he removes, there are at least four marbles of one colour and at least three marbles of another colour left in the bag, what is the maximum possible value of N?

\textbf{(A)}\ 6\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 10

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 Pascal contests here.