SHARYGIN 2016 Problem 7

Let all distances between the vertices of a convex $n$-gon ($n > 3$) be different. a) A vertex is called uninteresting if the closest vertex is adjacent to it. What is the minimal possible number of uninteresting vertices (for a given $n$)? b) A vertex is called unusual if the farthest vertex is adjacent to it. What is the maximal possible number of unusual vertices (for a given $n$)?