There cannot be exactly two parallel segments
Source: IMO Longlist 1989, Problem 36
September 18, 2008
combinatorics unsolvedcombinatorics
Problem Statement
Connecting the vertices of a regular -gon we obtain a closed (not necessarily convex) -gon. Show that if is even, then there are two parallel segments among the connecting segments and if is odd then there cannot be exactly two parallel segments.