2860.11 – Integer Sum of Unknown Length!

You're supposed to know that $\dfrac{1 + 2 + 3 + \ldots + n}{2} = \dfrac{n(n+1)}{2}$.

So all we need to do is set $\dfrac{n(n+1)}{6n} = 36$, and cross-multiply to get $n^2 + n = 216n$, a quadratic equation with roots $0$ and $215$. The latter root is the answer.