Consider a bar with N seats arranged in a line. A series of fat men enter the bar but each is too big for one seat, so he randomly picks a pair of adjacent unoccupied seats and sits on both. This continues until there are no longer any adjacent pairs of unoccupied seats at which point we look at the fraction f of the N seats which are occupied.
Question: What is the expected value of f (i.e., averaged over the random choice each man makes on where to sit) as N becomes infinite?