Problem #PRU-100228

Problems Algebra and arithmetic Graphs and locus of points on the Cartesian plane

Problem

There are 15 cities in a country named The Country of Fifteen Cities. The king ordered his main architect to build roads in such a way that each city was connected with other cities by exactly 5 roads, otherwise he would hang the architect. Do you think that the architect can accomplish the task or should he flee that country immediately?