A Mathematician's Holiday - Problem 1: Planning the tour.

Requirements:
Each participant should have a pencil, paper and rubber to draw and modify the diagram shown in Figure 2.

Description: 
In this activity we set the scene of the whole presentation. In particular, we talk about how all the activities were motivated by problems that we faced on our tour. The first problem is then, of course, organising the tour.

As mentioned previously we visited a number of locations around China and South Korea. These locations are shown in Figure 1.

Figure 1. All of the locations we visited on our tour.

Being huge tourists, we didn't want to have to travel between these locations in the same way twice, because each transportation route would allow us to see something different. In Figure 2 we represent each method of transportation by a black line between each of the cities. For example, the O and L mean Oxford and London and the two black lines represent the two different transportations of train and bus.

Figure 2. Representing the city connections.

The challenge is then to find a way around all the cities using all possible forms of transport. We found that we were not able to solve this problem. Can you? Of course the answer is contained in the video at the top.

Extension
From watching the video you should be able to see that identifying whether a set of paths are completely traversable with no repeating is pretty easy. However, suppose we specified the time each path took, how difficult would it be to find the quickest path around all cities?