The corridors of the labyrinth are the sides and diagonals of an n-sided convex polygon. How many light bulbs do we need to place in the labyrinth so that every passage is illuminated?
We will show that at least $n-1$ torches are necessary to light up the labyrinth. If, indeed, we place at most $(n-2)$ torches, then there will be a vertex that does not get a torch. From this vertex, $n-1$ corridors start, and any two of these have only this vertex as their common point. Since there is no torch here, at least $n-1$ torches are needed to light up these $n-1$ corridors. However, $n-1$ torches are clearly sufficient: if we place them in $n-1$ vertices, then every corridor will be lit, since a corridor always connects two vertices, and at least one of these will have a torch.