1) The Library of Babel consists of interconnecting hexagonal rooms. Each room contains 20 shelves,

with 35 books of uniform format on each shelf. A book has 410 pages, with

40 lines to a page, and 80 characters on a line, taken from an alphabet of 25 orthographic

symbols (22 letters, comma, period, and space). Assuming that 1 copy of every possible book

is kept in the library, how many rooms are there?---- is there enough information here to work out the number of rooms?

2) This two-player game requires a sheet of paper and pencils of two colors, say red and blue. Six points on

the paper are chosen, with no three in line. Now the players take a pencil each, and take turns drawing a

line connecting two of the chosen points. The ﬁrst player to complete a triangle of her own color loses.

Only triangles with vertices at the chosen points count. Can the game ever result in a draw? If yes,

describe the strategy. If not, explain why not