MathDB

There are

n

cities on each side of Hung river, with two-way ferry routes between some pairs of cities across the river. A city is “convenient” if and only if the city has ferry routes to all cities on the other side. The river is “clear” if we can find

n

different routes so that the end points of all these routes include all

2n

cities.
It is known that Hung river is currently unclear, but if we add any new route, then the river becomes clear. Determine all possible values for the number of convenient cities.
Proposed by usjl

Problem Statement