CAN YOU GET
THERE FROM HERE?
Towns A, B, and C are connected to each other by several roads, with at least one road connecting each pair of towns. In going from A to B one can go directly on one of the roads joining them, or one can travel from A to C on one of the roads joining A and C and then travel from C to B on a road joining C and B. In all, there are 33 routes from A to B (including those via C). Similarly, there are 23 routes from B to C (including those via A). How many routes are there from A to C (including those via B)?