MathDB

421

Part of 1986 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 421 All Soviet Union MO 1986 n cities, n-1 roads, shortest distances

Source:

8/6/2019
Certain king of a certain state wants to build nn cities and n−1n-1 roads, connecting them to provide a possibility to move from every city to every city. (Each road connects two cities, the roads do not intersect, and don't come through another city.) He wants also, to make the shortests distances between the cities, along the roads, to be 1,2,3,...,n(n−1)/21,2,3,...,n(n-1)/2 kilometres. Is it possible for
a) n=6n=6
b) n=1986n=1986 ?
combinatoricsdistance