14. Place the numbers $1,2,3,4,5$ in a circle. We call a placement method a "central ring" placement if for some number $n$ in the range 1 to 15, it is impossible to select several consecutive numbers on the circle such that their sum is $n$. If two placement methods are the same after rotation or reflection, they are considered the same method. How many "central ring" placement methods are there in total?
(Explanation: If placed as shown in the figure below, then $1-5$ can be taken as a single number, $6=5+1,7=3+4,8=5+1+2$, $9=2+3+4,10=1+2+3+4,11=5+1+2+3,12=4+5+1+2,13=3+4+5+1,14=2+3+4+5,15=1+2+3+4+5$, so all numbers from 1 to 15 are obtained, and this is not a "central ring" placement method.)
【Analysis】 $1,2,3,4,5$ and $15,14,13,12,11,10$ can definitely be taken; if 6 can be taken, then $15-6=9$, which cannot be taken; if 7 can be taken, then $15-7=8$, which cannot be taken; any of the above conditions being met is a valid placement method.
$$
\begin{array}{l}
6=1+5=2+4=1+2+3 ; \\
7=2+5=3+4=1+2+4 ;
\end{array}
$$

Without 6, (1,5 separated, 2,4 separated, and 1,2,3 not together), 1 way; without 7, (2,5 separated, 3,4 separated, and 1,2,4 not together), 1 way; in total, two ways.
As shown in the figure below