Hi. It's been awhile since I've had a math class, but it seems that Christopher is right... if you assume that both endpoints of both poles *have* to touch the walls of the alley. But you didn't state in the original problem that that is true. It would seem that - without all four endpoints of the poles touching wall - the minimum width of the alley approaches zero as the poles move towards the vertical (it can't actually *be* zero, because the poles have to cross), and the maximun width of the alley would approach 2 times the square root of 7.