Re: [math-fun] Ambiguously placed cities

I have now found may solutions to the ambiguous towns problem with 5 integers distances and 1 non-integer distance. These were found by first finding a parameterized family of solutions with 4 integer distances and 2 non-integer distances and then searching on this family. They all belong to the class of solutions illustrated in Eg Pegg's gif file picture. They are pretty ugly, here is one of the simpler ones: [AB,BC,CA,DA,DB,DC]= [70200, 219024, 2808*sqrt(6709), 70425, 5625, 224649] is planar and can be re-arranged to [AB,BC,CA,DA,DB,DC]= [70200, 219024, 2808*sqrt(6709), 5625, 70425, 224649] which is also planar. Jim Buddenhagen