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Travelling Salesman

Age 11 to 14
Challenge Level Yellow star
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A Hamiltonian circuit (named after the Irish mathematician Sir
William Rowan Hamilton) is a continuous path in a graph that
passes through each of the vertices exactly once and returns to
its starting point.

How many Hamiltonian circuits can you find in these graphs?

Here is another classic problem. A salesman lives in
city A and he has to visit the cities B, C and D. The distances
between the cities are: AB = 120, AC=140, AD=180, BC=70, BD=100,
CD=110. Find the shortest round trip from A through the other
three cities.


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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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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