a convex n gon
Source: Bulgaria TST 2003 P3
September 8, 2012
inductioncombinatorial geometrycombinatorics proposedcombinatorics
Problem Statement
Some of the vertices of a convex -gon are connected by segments, such that any two of them have no common interior point. Prove that, for any points in general position, there exists a one-to-one correspondence between the points and the vertices of the gon, such that any two segments between the points, corresponding to the respective segments from the gon, have no common interior point.