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4n Right Angles

Source: Iran TST 3, Day 1, Problem 2

May 12, 2013
geometryrectangleanalytic geometryinductioncombinatorics proposedcombinatorics

Problem Statement

we are given nn rectangles in the plane. Prove that between 4n4n right angles formed by these rectangles there are at least [4n][4\sqrt n] distinct right angles.
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