# Vertices required to construct a graph with at least $500$ edges

On our technique test, our educator offered us this trouble and also this solution:

What is the least variety of vertices called for to construct a full chart with at the very least $500$ sides? (Show your job yet do not try to streamline your solution way too much!)

Answer: We require to select $n$ such that $\dbinom{n}{2} \geq 500$.

I do not recognize just how she reached this solution. I attempted to begin with the definition of a full chart, yet where to go from there, I had no suggestion.

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2022-07-25 20:43:26
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