Combinatorics · Grid counting · Lattice rectangles · Casework
Vid cut a square \(ABCD\) of side length \(20\) units into \(400\) unit squares. Eva then picked four vertices of unit squares, all lying in the interior of \(ABCD\), that are the vertices of a rectangle whose sides are parallel to the sides of \(ABCD\); she picked them so that exactly \(24\) unit squares have at least one point in common with the sides of that rectangle. Determine all possible areas of such rectangles.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2010, 1. letnik, category A, problem 5. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source