1390 Ants near a line
Source: Argentina Cono Sur TST 2013, Problem 3
September 24, 2014
analytic geometrygeometryrectangleinequalitiesPythagorean Theoremcombinatorics proposedcombinatorics
Problem Statement
ants are placed near a line, such that the distance between their heads and the line is less than and the distance between the heads of two ants is always larger than . Show that there is at least one pair of ants such that the distance between their heads is at least meters (consider the head of an ant as point).