One case of a combinatorial optimization problem.
This problem is one which asks, given a list of multiple cities and distances between them, what is the shortest possible route that visits each city and returns to the city of departure? In this problem, when the number of cities equals N, the number of routes that pass through each of the cities becomes (N-1)!/2. As one can see from this equation, as N increases, the number of possible routes increases explosively.
