IMO 1969 LL FRA20

A polygon (not necessarily convex) with vertices in the lattice

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IMO 1969 LL FRA20

Origin: FRA

Problem

A polygon (not necessarily convex) with vertices in the lattice points of a rectangular grid is given. The area of the polygon is S. If I 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.