In the coordinate system in the plane we consider a convex polygon W and lines given by equations x=k,y=m, where k and m are integers. The lines determine a tiling of the plane with unit squares. We say that the boundary of W intersects a square if the boundary contains an interior point of the square. Prove that the boundary of W intersects at most 4 \lceil d \rceil unit squares, where d is the maximal distance of points belonging to W (i.e., the diameter of W) and \lceil d \rceil is the least integer not less than d. analytic geometryceiling functioncombinatorics unsolvedcombinatorics