Problem #PRU-100418

Problems Algebra Graphs and locus of points on the Cartesian plane

Problem

There are six cities in Wonderland. Her Majesty’s principal secretary of state for transport has a plan of building six new railways. The only condition for these railways is that each of them joins some pair of cities having other four cities equally distributed on both sides of a line containing the segment of the railway. Is it possible to implement such a plan for some configuration of cities?