very hard(Russia 2003)(help me)
Source: V. Dolnikov, P. Karasev
August 5, 2009
analytic geometryemailgeometrygeometric transformationhomothetycombinatorics unsolvedcombinatorics
Problem Statement
A finite set of points and an equilateral triangle are given on a plane. Suppose that every subset of with no more than elements can be covered by two images of under translations. Prove that the whole set can be covered by two images of under translations.