Traveling Salesman In the famous Traveling Salesman Problem, a salesman starts in any one of a set of cities, visits every city in the set once, and returns to the starting city. He would like to complete this circuit with the shortest possible distance.
(a) Suppose the salesman has 10 cities to visit. Given that it does not matter what city he starts in, how many different circuits can he take?
(b) The salesman decides to check all the different paths in part (a) to sec which is shortest but realizes that a circuit has the same distance whichever direction it is traveled. How many different circuits must he check?
(c) Suppose the salesman has 70 cities to visit. Would it be feasible to have a computer check all the different circuits? Explain your reasoning.
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Finite Mathematics (11th Edition)
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