TOT 004 1980 Spring J4 S4 sum of areas in a grid NxN of random convex ABCD
Source:
August 16, 2019
areasgeometry
Problem Statement
We are given convex quadrilateral . Each of its sides is divided into line segments of equal length. The points of division of side are connected with the points of division of side by straight lines (which we call the first set of straight lines), and the points of division of side BC are connected with the points of division of side by straight lines (which we call the second set of straight lines) as shown in the diagram, which illustrates the case .
This forms smaller quadrilaterals. From these we choose quadrilaterals in such a way that any two are at least divided by one line from the first set and one line from the second set. Prove that the sum of the areas of these chosen quadrilaterals is equal to the area of divided by . (A Andjans, Riga)
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