MathDB
BMT 2021 General p5

Source:

September 27, 2023
combinatorics

Problem Statement

Bill divides a 28×3028 \times 30 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 11 unit away from either of the edges with length 2828 will result in the same pair of boards: either way, one would end up with a 1×281 \times 28 board and a 29×2829 \times 28 board.)