I am trying to prove the following:
Let $c(n)$ be the minimum number of cameras, where each is seen by at least one other camera. Now $c(n)$ is always sufficient and sometimes necessary for watching an $n$-walled gallery which is orthogonal. Prove that $c(n)$ is equal to $\left \lfloor{\dfrac{n}{e}}\right \rfloor$.
I know of the art gallery problems and that for an orthogonal polygon, only $\left \lfloor{\dfrac{n}{4}}\right \rfloor$ guards are needed. I have not been able to figure out how to prove this problem. More specifically, I am not sure where or how the $e$ comes in to play.
I would appreciate some hints/guidance on this. Thank you.