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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

Try drawing these maps without lifting your pencil

What do you notice about the start and end positions?

- Now consider these

What do you notice about the start and end positions now?