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Plane figure with area > n can cover n + 1 lattice points

Source: Mediterranean MO 1999

October 11, 2012
geometrypigeonhole principleanalytic geometrycombinatorics unsolvedcombinatorics

Problem Statement

A plane figure of area A>nA > n is given, where nn is a positive integer. Prove that this figure can be placed onto a Cartesian plane so that it covers at least n+1n+1 points with integer coordinates.
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