Ahhh, the 'harmonic' workings of large numbers... here's a recent paradoxical braintwister from "Futility Closet":
(The problem can be found at Wikipedia for those who want a fuller explanation of the counter-intuitive result: http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope ...the key is to understand the full "elastic" nature of the band).
The 'Futility' problem reminds me a tad of a more complicated Raymond Smullyan puzzler that I love and have posted here before:
--> Addendum note: in a nice little bit of coincidence, I just discovered that Jason Rosenhouse posted a short while back that he will be editing a tribute book to Raymond Smullyan due out sometime next year from Dover Publications. Great news!