rainbow@ihuxe.UUCP (08/21/84)
<sacrificial line> > How many places can one walk X miles south, then X miles west, and return > to your starting point by walking X miles north. The obvious place is the north pole. But there are an infinite number of more places where this can be done. Consider the ring near the south pole where the circumference of the earth is X miles. In other words walking in a west- word direction will take you completely around once(the solution can be expanded to include rings which make any number of exact loops in X miles). Now consider the infinite points which are X miles north of the ring in consideration. Start your journey here.