7. Four towns $P, Q, R$ and $S$ are connected by roads, as shown. A race uses each road exactly once. The race starts at $S$ and finishes at $Q$. How many possible routes are there for the race?
A 10
B 8
C 6
D 4
E 2
7. C Any route starts by going from $S$ to $P$ or $S$ to $Q$ or $S$ to $R$. Any route starting $S$ to $P$ must then go to $Q$ and then has the choice of going clockwise or anticlockwise round triangle $Q S R$, giving two possible routes. By a similar argument, there are two routes that start $S$ to $R$. For those routes that start by going from $S$ to $Q$, there is then the choice of going clockwise or anticlockwise round quadrilateral $Q P S R$, giving two more routes. Therefore there are six possible routes in total.