AMC 10 2014b Problem 24

The numbers $1, 2, 3, 4, 5$ are to be arranged in a circle. An arrangement is $\textit{bad}$ if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there? $\textbf {(A) } 1 \textbf {(B) } 2 \textbf {(C) } 3 \textbf {(D) } 4 \textbf {(E) } 5$ .