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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?

two diagrams of nodes with lines joining them

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.