Note: Some people have complained that the problem is not easy to solve because the figures are hand-drawn, hence it is not easy to see that the circumference of one circle passes through the center of the other. Sorry, I simply scanned the figures that D. R. Hofstadter hand-drew with a pencil on a low-quality paper -- and I scanned a photocopy of that, to boot. I thought that re-drawing these problems with an image-drawing program would kill some of the flavor of originality in them.