Combinatorics · Pigeonhole principle · Area argument · Translation
A plane figure of area greater than \(1006\) can be placed inside a rectangle with side lengths \(2011\) and \(1\). Prove that the figure contains two points, on its boundary or in its interior, whose distance is exactly \(1\).
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Serbian Regional Competition 2011, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source