Welcome to Probistis Mu
Welcome to Probistis Mu. We hope you'll enjoy the wonderful sights of our world, from the Truly Infinite Corridor in the city of NelpNelpNelpNelpNelp... to the Klein Bottle Rotunda in our capital (located at beta on the map), as well as the tourist attractions in the other 13 cities of Probistis Mu. To obtain a map of our world, please contact headquarters.
After you do, you can help us out with a dilemma we have. We are supposed to deliver a sign to each of our 15 cities, but need help figuring out which city gets which sign. On the map, the distance between any two dark circles, or any dark circle and city, is exactly one mile. However, many of our citizens are superstitious about traveling on the switchback roads that travel over the "edge of the world" (such as the 2-mile road that connects alpha and pi). Thus, the top figure on each sign is the shortest distance to the named city without using any switchback roads. The bottom figure is the shortest distance to the other named city, using these switchback roads if necessary.
Once you assign a sign per city (which are lettered on the map for convenience only), perhaps you can further help us by filling in the missing city names on the last two signs. Do that, and you may even discover the name of the one city that isn't listed on any of the signs at all!