One of the main reasons for this challenge is to find ways of approaching such a problem. When introducing it to the class, it would be good to put the problem into a context, perhaps by talking first about local journeys. You could ask the children if they have ever seen maps of train/bus/tram/underground routes drawn in stations or on the walls of the vehicles themselves. It would be good to
discuss how the maps are "models" for the routes taken - they are simply a way to put the routes on paper to make it easy to understand.
You could then show your pupils the route in the problem and ask a few questions about it so that you are sure they understand the way it is drawn. For example, if I came from Appleby, what station would the train stop at after Barkton? (This could be Worsby or Xanly.) You might like to begin the first part of the problem as a whole class, asking them how they will know when they have all the
different routes. How will they record the routes that they find? This is a good opportunity to model having a system. Your class might suggest several routes from Appleby to Cheston, and you could pair them up so that the two which both visit Yanbridge, for example, are together. In this way, even if this time they have not found them systematically in the first place, the children can see how
they can develop a system next time.
Children might like to try the investigation Simple Train Journeys
after having a go at this problem, which uses similar ideas but in a more open context.