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No four chosen vertices form trapezium or rectangle

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December 31, 2011
geometrytrapezoidrectangleparallelogramcombinatorics unsolvedcombinatorics

Problem Statement

Consider 201122011^2 points arranged in the form of a 2011×20112011 \times 2011 grid. What is the maximum number of points that can be chosen among them so that no four of them form the vertices of either an isosceles trapezium or a rectangle whose parallel sides are parallel to the grid lines?
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