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Usenet Newsgroups : rec.puzzles Hall of Fame


The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

   
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Categories : pickover : pickover.02.p

Title: Cliff Puzzle 2: Grid of the Gods
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please include your name,
address, affiliation, e-mail address.  If you like, tell me a little bit
about yourself.  You might also directly mail me a copy of your response
in addition to any responding you do in the newsgroup.  I will assume it
is OK to describe your answer in any article or publication I may write
in the future, with attribution to you, unless you state otherwise.
Thanks, Cliff Pickover

* * *

Consider a grid of infinitesimal dots spaced 1 inch apart in a cube with
an edge equal in length to the diameter of the sun (4.5x10**9 feet).
For conceptual purposes, you can think of the dots as having unit
spacing, being precisely placed at 1.00000...., 2.00000....,
3.00000...., etc. Next choose one of the dots and draw a line through it
which extends from that dot to the edge of the huge cube in both
directions.

Stop And Think

1. What is the probability that your line will intersect another dot
in the fine grid of dots within the cube the size of the sun?
Would your answer be different if the cube were the size of the
solar system?

2. Could a computer program be written to simulate this process?

3. Answer the two questions above, but this time assume the line
to have some finite thickness, T.



Solution


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