Math and Logic

How Much Can They See?

Art gallery problems involve finding an unmoving guard (or guards) who can "see" the entire gallery. A guard is able to see any part of the gallery that can be connected to its position by a straight line without intersecting any walls.

The solution of the problem depends on the shape of the polygon, but the relationship between a polygon's properties and the number of guards required is tricky. For example, two of the concave polygons below can be guarded by a single guard, but the other one requires two guards. Can you tell which one?