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number of rectangles by lattice vertices

Source: Greece Junior Math Olympiad 2023 p3

March 2, 2024
geometrycombinatoricscombinatorial geometrylattice points

Problem Statement

Find the number of rectangles who have the following properties: a) Have for vertices, points (x,y)(x,y) of plane OxyOxy with x,yx,y non negative integers and x≤8 x \le 8 , y≤8y\le 8 b) Have sides parallel to axes c) Have area EE, with 30<E≤4030<E\le 40
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