A rectangular floor measures by feet, where and are positive integers with . An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair ?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email email@example.com.