Question 27
Let $n_1,n_2,n_3,\ldots,n_9$ be nine distinct positive integers such that $n_1\lt n_2\lt n_3\lt \cdots\lt n_9$ and $n_1+n_2+n_3+\cdots+n_9=180$. Suppose that the value of $n_1+n_2+n_3+n_4+n_5$ is maximum, find the maximum possible value of $n_9-n_1$.