5 points in the plane so that among all there are 8 right-an
Source: JBMO 2005, Problem 3
October 29, 2005
combinatorics proposedcombinatorics
Problem Statement
Prove that there exist
(a) 5 points in the plane so that among all the triangles with vertices among these points there are 8 right-angled ones;
(b) 64 points in the plane so that among all the triangles with vertices among these points there are at least 2005 right-angled ones.