Minimal number of edges in an directed graph that ensures the existence of a cycle

Question

I need to find the minimal number of edges in an directed graph with $n$ vertices, that ensures the existence of a cycle in the graph, and proof that for every directed graph with $n$ vertices and that number of edges (or more) there is a cycle.

I tried to find it for small values of $n$ and find a pattern, but even this didn't work.

Answer 1

Hint: show that you can put one edge between every pair of vertices without creating a cycle.