Same as German TST
Source: French TST 2004 pb.3
May 25, 2004
analytic geometryinequalitiespigeonhole principletriangle inequalitycomplex numbersgeometry proposedgeometry
Problem Statement
Each point of the plane with two integer coordinates is the center of a disk with radius .
Prove that there exists an equilateral triangle whose vertices belong to distinct disks.
Prove that such a triangle has side-length greater than 96.