BG-MO 1986 Problem 4

Find the smallest integer $n\ge3$ for which there exists an $n$ -gon and a point within it such that, if a light bulb is placed at that point, on each side of the polygon there will be a point that is not lightened. Show that for this smallest value of $n$ there always exist two points within the $n$ -gon such that the bulbs placed at these points will lighten up the whole perimeter of the $n$ -gon.