Question 85
Each of the integers $1,2,3, \ldots, 9$ is assigned to each vertex of a regular 9-sided polygon (that is, every vertex receives exactly one integer from $\{1,2, \ldots, 9\}$, and two vertices receive different integers) so that the sum of the integers assigned to any three consecutive vertices does not exceed some positive integer $n$. What is the least possible value of $n$ for which this assignment can be done?