Trains @ Königsberg
The above image represents a map of Königsberg. The green areas are land and the yellow lines are bridges.
The emperor of the kingdom wants to set up a train service that transports people from a landmass to another within the empire using the bridges.
There are people in the red castle who want to go to the blue castle subject to the following conditions:
- The route cannot traverse a bridge twice.
- The route can visit a landmass numerous times, including the land of the red castle.
- The route stops the first time it reaches the blue castle.
How many possible train routes could they take?