Recall that the *Cantor set* is obtained by taking the unit interval
[0,1] removing the "middle third" (namely the interval (1/3, 2/3)), then
the two "middle thirds" of the remaining intervals (namely the intervals
(1/9, 2/9) and (7/9, 8/9)), then the four "middle thirds", etc., etc., ad
infinitum, as shown in the figure below.

This month's problem is to find the __average__ distance between two
points in the Cantor set.