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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.