CAYLEY 2018 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

Answer Choices
A. 48
B. 72
C. 64
D. 80
E. 56