A ladybug is walking at random on a hexagon. She starts at vertex $A$. Every minute, she moves to one of the two vertices (chosen at random) adjacent to the one she's currently on. What is the probability that, after $10$ minutes, she is back at $A$

On traditional maps, earth is represented in a flat plane, or by euclidean geometry. however, a globe is a more accurate model that comes from elliptical geometry.how does a globe represent the fact that there are no parallel lines in elliptical geometry? the equator is not parallel to any other latitudinal lines. the north and south poles are never connected by a geodesic. the geodesics connecting the north and south poles never intersect. the geodesics connecting the north and south poles intersect at both of the poles.