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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.
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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?