8. A ladybird aims to travel from hexagon $\mathrm{X}$ to hexagon $\mathrm{Y}$, passing through each of the seven unshaded hexagons once and only once. She can move from one hexagon to another only through a common edge. How many different routes could she take?
A 2
B 3
C 4
D 5
E 6
Solution
D

Any such route will need to travel anticlockwise around the outer ring of unshaded hexagons. At some point the ladybird must enter the central hexagon and then exit it to the next available outer hexagon. There are five points at which the ladybird could enter the central hexagon (since she cannot do it from the final unshaded hexagon), and each gives a different route, hence five routes.