St. Ives Problem/Solution 2

Solution
Trick question aside, one can suppose that in order for the narrator to find out all about the unusual nature of this man's ménage, he would have had to spend some considerable time in his company, more than just a tip of the hat as they passed each other.

Hence it can be assumed that they met at a meeting of the ways, for example, when the narrator's path merged with that of the man and his family, and they travelled to St. Ives together.

So the number of entities mentioned in the riddle are counted as follows:

This is a geometric progression:

... ... and don't forget the narrator (a surprising number of the treatments of this subject do just that):
 * $2 \, 802$

Quite a crowd.