Road Trip Problem

A group of Xavier students decides to travel together from Cincinnati over spring break. They want to visit each of their hometowns. No one wants to visit their hometown more than once and they want to return to Cincinnati at the end of the trip. Here is a map including mileage:
  1. Determine the shortest route the students can take.
  2. What algorithm did you use to determine the route?
  3. Will that algorithm always work?
  4. Is there an algorithm that will always work? If so, what is its order of magnitude?