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Relation between boundary, interior points and area

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September 29, 2010
geometrypolygonlattice pointsareaIMO ShortlistIMO Longlist

Problem Statement

(FRA3)(FRA 3) A polygon (not necessarily convex) with vertices in the lattice points of a rectangular grid is given. The area of the polygon is S.S. If II is the number of lattice points that are strictly in the interior of the polygon and B the number of lattice points on the border of the polygon, find the number T=2S−B−2I+2.T = 2S- B -2I + 2.
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