Solution for #35

The circumference of a circle is 2πr, where r is the radius of the circle. If you want a rope that is one yard above the ground, this radius is larger by one yard. Let R be this new radius. So R = r + 1.

Let x be the amount of extra rope required by the eccentric's rival. So:

     x = (2π(r + 1)) - (2πr)
     x = (2πr) + (2π) - (2πr)
     x = 2π 

So x is about 6.2832 yards. Note that this answer does not depend on the radius of the circle. If the eccentric and his rival were attempting to tie up a baseball rather than the earth, the amount of additional required rope would be the same amount.