2018 Cayley Problem 25

There are N sequences with 15 terms and the following properties:

- each term is an integer, - at least one term is between -16 and 16, inclusive, - the 15 terms have at most two different values, - the sum of every six consecutive terms is positive, and - the sum of every eleven consecutive terms is negative.

The value of N is

\textbf{(A)}\ 48\quad \textbf{(B)}\ 72\quad \textbf{(C)}\ 64\quad \textbf{(D)}\ 80\quad \textbf{(E)}\ 56

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.