Uninteresting and unusual convex n-gon
Source: Sharygin Geometry Olympiad Correspondence round 2016 P-7 Grade 8-9
February 20, 2017
geometrycombinatorics
Problem Statement
Let all distances between the vertices of a convex -gon () 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 )?
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 )?(Proposed by B.Frenkin)