2005 Cayley Problem 15

Starting with the 2 in the centre, the number 2005 can be formed by moving from circle to circle only if the two circles are touching. How many different paths can be followed to form 2005?

\textbf{(A)}\ 36\quad \textbf{(B)}\ 24\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 18\quad \textbf{(E)}\ 6

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.