Imagine you're standing on a set point on the surface on the outer coin, e.g. the one touching the inner coin. As the outer coin rotates around the inner coin, your experienced reality will be that you see n-1 rotations.

In the example of the outer coin having 1/3 the radius of the inner coin, as the outer coin rolls around the inner coin 4 times, you would actually only touch the inner coin 3 times.