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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.06.p

Title: Cliff Puzzle 6: Star Chambers
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
address, affiliation, e-mail address.  If you like, tell me a little bit
about yourself so I can cite you appropriately if you provide unique
information.  PLEASE 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

* * *

As many of you probably know, 5-sided stars produced by drawing a
continuous line with your pencil can nest inside each other.  (One star
can sit inside the pentagon produced by the larger star.  Each of the
5 points of the small star coincide with the 5 points of the
internal pentagon of the large star.)

Start with a five sided star formed with 5 line segments, each 1 inch
long.  Continually nest stars so that the assembly of stars gets bigger
and bigger.

Questions:
1.  How many nestings N are required to make star N
have an edge-length equal to the diameter of the sun (4.5E9 feet)?

2. How many nestings N are required to make the cumulative length
of lines of all the nested stars equal to the diameter of the sun?



Solution

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