Find all possible values for the area [Slovenia 2010]
Source:
November 14, 2010
geometryrectanglecombinatorics proposedcombinatorics
Problem Statement
Let be a square with the side of units. Amir divides this square into unit squares. Reza then picks of the vertices of these unit squares. These vertices lie inside the square and define a rectangle with the sides parallel to the sides of the square There are exactly unit squares which have at least one point in common with the sides of this rectangle. Find all possible values for the area of a rectangle with these properties.[hide="Note"]Note: Vid changed to Amir, and Eva change to Reza!