substantially different decompositions of 2010x2010 square into 3 rectangles
Source: 41st Austrian Mathematical Olympiad National Competition (Final Round, part 2) 3rd June 2010 p5
September 5, 2019
geometryrectanglecombinatoricscombinatorial geometry
Problem Statement
Two decompositions of a square into three rectangles are called substantially different, if reordering the rectangles does not change one into the other.
How many substantially different decompositions of a square in three rectangles with integer side lengths are there such that the area of one rectangle is equal to the arithmetic mean of the areas of the other rectangles?