The diagram below shows a network of train lines between five towns: Attard, Bower, Clement, Derrin and Eden.
The numbers indicate the distances, in kilometres, that are travelled by train between connected towns.
Charlie followed an Eulerian path through this network of train lines.
- i. Write down the names of the towns at the start and at the end of Charlie’s path. (1 mark)
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ii. What distance did he travel? (1 mark)
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Brianna will follow a Hamiltonian path from Bower to Attard.
- What is the shortest distance that she can travel? (1 mark)
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The train line between Derrin and Eden will be removed. If one other train line is removed from the network, Andrew would be able to follow an Eulerian circuit through the network of train lines.