Please read the short story “The Library of Babel” by J. L. Borges. In summary, it is the story of a large library containing books with all possible combinations of 25 symbols. Each line has 80 characters, there are 40 lines on each page and 410 pages on each book.
- How many words are, on average, on each book?
- How may books are there in The Library? It is ok to give an approximate number if you indicate the margin of error.
- How many rooms are in the library? Remember that each room has shelves in 4 walls and there are five shelves on each wall, with 32 books on each. (The rooms are hexagonal, so there are two other walls with doors connecting to other rooms.)
- What area is covered by such a library? Remember that the area of a hexagon of side \(s\) is \(3\sqrt{3} s^2/2\).
- If this library exists in a planet like Earth, how many floors does it need?
- Bonus: What is the weight of the library? How many trees are needed to make the paper for the books?
This is a question about handling large numbers.