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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.12.p

Title: Cliff Puzzle 12: Slides in Hell
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
address, affiliation, e-mail address, so I can properly credit you 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

      * * *

Consider a metallic slide with 10 large holes in it equally spaced from
top to bottom.  If you attempt to slide down the slide you have a 50%
probability of sliding through each hole in the slide into an oleaginous
substance beneath the slide during each encounter with a hole.

1.  If you were a gambling person, which hole would you bet a person
would fall through?

2.  If you were a gambling person, how many attempts would it require
for a person to slide from the top of the slide to the bottom without
falling through a single hole.

3.  If all the people on earth lined up to go down the slide, and they
slid down a more horrifying slide with 100 holes at a rate of 1 person
per second, when would you expect the first person to arrive at the
bottom of the slide without falling through.
An hour? A day? A decade? ...
Received: from uoft02.utoledo.edu by watson.ibm.com (IBM VM SMTP V2R2) with TCP;
Title: Cliff Puzzle 12: Slides in Hell
>Consider a metallic slide with 10 large holes in it equally spaced from
>top to bottom.  If you attempt to slide down the slide you have a 50%
>probability of sliding through each hole in the slide into an
>oleaginous substance beneath the slide during each encounter with a
>hole.
>
>1.  If you were a gambling person, which hole would you bet a person
>would fall through?

None.  The best chance is the first hole but I got a 50-50 chance.  Why
bother?  (2nd hole is 1/4, 3rd 2**-3, ...)

>2.  If you were a gambling person, how many attempts would it require
>for a person to slide from the top of the slide to the bottom without
>falling through a single hole.

No gurantee.  Each slide is an independent event.  Now, if you are
talking mere probability, on the average, one in 1024 slides may make
it through all 10 holes.

>3.  If all the people on earth lined up to go down the slide, and they
>slid down a more horrifying slide with 100 holes at a rate of 1 person
>per second, when would you expect the first person to arrive at the
>bottom of the slide without falling through.  An hour? A day? A decade?

Again, can't tell.  It could be the first one, it could be none.  Probablity
can not foretell actual events.  But if you have infinite number of people
sliding down till eternity, on the average, you may see 1 person slide over
all holes every (2**100)/(365*24*69*6) years.  This number is many times
bigger than the world population for now.


Solution


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