BMT 2021 General p5
Source:
September 27, 2023
combinatorics
Problem Statement
Bill divides a rectangular board into two smaller rectangular boards with a single straightcut, so that the side lengths of both boards are positive whole numbers. How many different pairs of rectangular boards, up to congruence and arrangement, can Bill possibly obtain? (For instance, a cut that is unit away from either of the edges with length will result in the same pair of boards: either way, one would end up with a board and a board.)