On our practice exam, our teacher gave us this problem and this solution:
What is the fewest number of vertices required to construct a complete graph with at least $500$ edges? (Show your work but do not attempt to simplify your answer too much!)
Answer: We need to select $n$ such that $\dbinom{n}{2} \geq 500$.
I do not understand how she got to this answer. I tried to start with the definition of a complete graph, but where to go from there, I had no idea.