Mapping Puzzle Answer

The maximum number of towns that any town can be connected to is 5. Think of the town as the center of spokes on a wheel. Six towns would give you a regular hexagon, but the six towns on the perimeter of the wheel would be the same distance from each other as they are from the town at the center of the wheel. That is not allowed.

Five spokes would give you a pentagon with the spokes 15% shorter than the average distance between the five towns on the perimeter.