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Only Connect

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Travelling Salesman

Age 11 to 14 Challenge Level:

Mathematicians have found no general criterion to test
whether a graph contains a Hamiltonian circuit or not. This is
unfortunate because there are many important questions in graph
theory which depend on the existence or non-existence of
Hamiltonian circuits.