MathDB

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.

Problem Statement