This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2015 JBMO TST - Turkey, 3
Tags: graph theory , flights , combinatorics
In a country consisting of $2015$ cities, between any two cities there is exactly one direct round flight operated by some air company. Find the minimal possible number of air companies if direct flights between any three cities are operated by three different air companies.

2019 Philippine TST, 1
Tags: combinatorics , flights , graph theory
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 $A$ to $B$ and also none from $B$ to $A$, or there is a unique [i]two-way trip[/i] between them. A [i]two-way trip[/i] is a flight from $A$ to $B$ and a flight from $B$ to $A$. 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.