Problem #75

A hemisphere of radius 1 rests on a table. There are n hemispherical caps stacked on top of it with the equator of each sphere resting on the surface of the one below it (the diagram below illustrates the case n = 2). If the radii of the n hemispherical caps vary (but the hemisphere of radius 1 remains unchanged), what is the maximum possible height of the stack for a given n?

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