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Icosian Game

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Travelling Salesman

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

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Tourism

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Königsberg

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

You may like to download this word document which helps to explain the diagrammatic representation and provides blank diagrams and maps with no bridges for further investigation.

This lesson plan suggests how you could introduce this problem in the classroom.