Prove that there exist two vectors [ILL 1974]
Source:
January 2, 2011
vectorgeometrygeometric transformationcombinatorics unsolvedcombinatorics
Problem Statement
There are points on a flat piece of paper, any two of them at a distance of at least from each other. An inattentive pupil spills ink on a part of the paper such that the total area of the damaged part equals . Prove that there exist two vectors of equal length less than and with their sum having a given direction, such that after a translation by either of these two vectors no points of the given set remain in the damaged area.