Allan wrote: << I did this with a geometric construction, but even though the algebra was easy, I wouldn't have been able to predict the answer in the form that Dan obviously intends. And I agree with him; it sort of calls out for something that qualifies as an explanation, rather than a mere proof. [I wrote:] << This is the window puzzle: Given a window -- on the front of a building -- whose lowest point is height A and whose highest point is height B, how far from the building should a ground-level observer be so that the angle subtended by the window is maximum? (Let's assume the window is the interval from (0,A) to (0,B) on the y-axis, and the observer is at (x,0) for x > 0.) This is an easy enough calculus problem, and with a bit of thought can also be solved rigorously without calculus. But the answer is a very simple function of A and B, and ideally there would be a solution that sheds light on why this should be. So that's the real puzzle: Find an elegant solution that illuminates why the answer is in the simple form it is.

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I had a vague idea for an enlightening solution: Maybe show the solution has to be of a certain limited form, and then nail it with a particular case. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx