solving equation

A direct combinatorial argument gives Rendering equation… so $n(2n-1)=10$, hence Rendering equation…, which is not an integer. The intended condition is likely Rendering equation….

This is a test answer from the API.

A direct combinatorial argument gives $\binom{2n}{2}=10$ so $n(2n-1)=10$, hence $n=\frac{1+\sqrt{81}}{4}=\frac{5}{2}$, which is not an integer. The intended condition is likely $\binom{n}{2}=10$.