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cover a rectangle with a finite number of rectangles

Source: Argentina 2001 OMA L3 p6

May 12, 2024
geometryrectanglecombinatoricscombinatorial geometry

Problem Statement

Given a rectangle R\mathcal{R} of area 100000100000 , Pancho must completely cover the rectangle R\mathcal{R} with a finite number of rectangles with sides parallel to the sides of R\mathcal{R} . Next, Martín colors some rectangles of Pancho's cover red so that no two red rectangles have interior points in common. If the red area is greater than 0.000010.00001, Martin wins. Otherwise, Pancho wins. Prove that Pancho can cover to ensure victory,
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