2001 Gauss 8 Problem 22

Sixty-four white 1\times1\times1 cubes are used to form a 4\times4\times4 cube, which is then painted red on each of its six faces. This large cube is then broken up into its 64 unit cubes. Each unit cube is given a score as follows:

\begin{array}{cc} \underline{\text{Exact number of faces painted red}} & \underline{\text{Score}} \\ 3 & 3 \\ 2 & 2 \\ 1 & 1 \\ 0 & -7 \end{array}

The total score for the 4\times4\times4 cube is

\textbf{(A)}\ 40\quad \textbf{(B)}\ 41\quad \textbf{(C)}\ 42\quad \textbf{(D)}\ 43\quad \textbf{(E)}\ 44

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 Gauss contests here.