dimensions of max of squares filling a rectangle by half
Source: JBMO 2011 Shortlist C7
October 14, 2017
JBMOcombinatoricscombinatorial geometry
Problem Statement
Consider a rectangle whose lengths of sides are natural numbers. If someone places as many squares as possible, each with area , inside of the given rectangle, such that the sides of the squares are parallel to the rectangle sides, then the maximal number of these squares fill exactly half of the area of the rectangle. Determine the dimensions of
all rectangles with this property.