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Set of rectangles - [IMO LongList 1971]

Source:

January 1, 2011
geometryrectangleanalytic geometrygeometry unsolved

Problem Statement

An infinite set of rectangles in the Cartesian coordinate plane is given. The vertices of each of these rectangles have coordinates (0,0),(p,0),(p,q),(0,q)(0, 0), (p, 0), (p, q), (0, q) for some positive integers p,qp, q. Show that there must exist two among them one of which is entirely contained in the other.
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