No such A, B sets exist
Source: Iran Third Round 1996, E1, P4
March 27, 2011
combinatorics proposedcombinatorics
Problem Statement
Show that there doesn't exist two infinite and separate sets of points such that(i) There are no three collinear points in ,(ii) The distance between every two points in is at least , and(iii) There exists at least one point belonging to set in interior of each triangle which all of its vertices are chosen from the set , and there exists at least one point belonging to set in interior of each triangle which all of its vertices are chosen from the set .