AoPS Wiki talk:Problem of the Day/July 28, 2011

Solution

The distances the ball bounces form a geometric sequence. The sequence goes infinitely (each, except for the 24, is duplicated because the ball goes up inches, and comes back down inches). If we add together the terms that are the same (and add a 24 to the beginning for the sake of a nice pattern), we get . Thus, our solution is .