An n-dimensional sphere of radius one is intersected with another
n-dimensional sphere of radius one and whose center lies on the
first sphere. The intersection is a (n-1)-dimensional sphere.

The (n-1)-dimensional sphere is intersected with another
n-dimensional sphere of radius one and whose center lies on the
(n-1)-dimensional sphere. The intersection is a (n-2)-dimensional sphere.

This procedure is continued until we have a 1-dimensional sphere.
What is its radius?

This all takes place in an n-dimensional space.