Pentagon Island has one airport located in the town of Winchester. A railroad links the five cities on the island -- Winchester, Bennettsville, Columbus, Flint, and Ventura. The track forms a complete loop, and trains run in both directions (see the diagram below).
When you land at the airport in Winchester, you are given a free pass, for eight trips on the train, between one town and the next. In how many different ways can you make a trip of exactly eight trips, starting and ending in Winchester?
If you are thinking that it is impossible to use all 8 tickets -- here is one possible trip: W - B - W - B - W - B - W - B - W.