MathDB

Let

n

and

\ell

be integers such that

n \ge 3

and

1 < \ell < n

. A country has

n

cities. Between any two cities

A

and

B

, either there is no flight from

A

B

and also none from

B

A

, or there is a unique two-way trip between them. A two-way trip is a flight from

A

B

and a flight from

B

A

. There exist two cities such that the least possible number of flights required to travel from one of them to the other is

\ell

. Find the maximum number of two-way trips among the

n

cities.

Problem Statement