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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?

Only Connect

Age 11 to 14
Challenge Level

The graph below represents a salesman's area of activity with shops at A, B, C, D, E and F. (It isn't drawn to scale.)

Map of towns and distances

The numbers represent the distance in kilometres between the places that salesman must visit each day.

What route around the shops has the minimum total distance?