Very easy but tricky

not x times celestine

see we have to cover all the vertices of the polygon wont we ?

we see that when we choose x we automatically have to choose another x-1

so let us complete choosing all vertices when we choose let a ..

then automatically we get another a-1

so

a+a-1=2n

thus a contradiction

yes but still cant make sense of #3

x -1 things repeated x times is x(x-1) right ??

i considered the vectors as the ones joining the fox and the vertices of the polygon

oh i took it carelessly earlier

now i got the fact :) .. good approach

yeah. let it intersect.
then number of lines going below the diagonal shown decreases, isn't it . so we have at most n-1 lines going below.

if the fox is little above then the line from n will intersect in the upper half ...

Sorry my mistake in typing . consider bullets from upper vertices.

Dont see the solution now:

Solution:
The fox , not on any diagonal is in one half of the polygon(i.e. above or below the diagonal joining 1st and (n+1)th vertices).let it be in upper half.
Then there are at most (n-1) bullets from above hitting n sides below. so atleast one side unharmed.

a more elegant one?

hmm let me think ..

Come on b555. I would like to see your solution.
Anyway, there is an elegant non-counting mathematical solution

oh! sorry !