>There are 100 books on the table. Some opened, some closed. The first person comes into the room and closes open books and open closed. The second does the same, but with all even books. The third does it for each 3rd number, etc. 100 people came to the room. The quesiton is: how many open books would be on the table after all 100 people have been in the room?

10, but I won't say how I got it.

What if it were 1000 books?