the library of babel question! and one other..

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