7. A translation of a planar region S is a rigid shift of it: add a constant vector to all points in S. An integer translation is a shift by an integer vector. For instance, if D is a disk of radius 1/3 centered at the origin, then any disk of radius 1/3 centered at a lattice point is an integer translation of D. Lemma. If Area(S) > 1, then some nonzero integer translation of S must overlap S.

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