> So what knowledge have you actually learned after the first round?

That your friend sees 2 or more, and your friend knows you see 18 or less. By itself, this is trivially deducable; but each day walks the limits closer to revela a fact that isn't trivial. You start the puzzle knowning that your friend can see either 6 or 8 statues, and each day you add a new fact about how many statues she can't see.

I'm more concerned that the problem as stated can be solved in 2 days: you say 18 on day one, then 20 on day two…