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From: tan@ihlpg.UUCP (Bill Tanenbaum)
Newsgroups: net.puzzle
Subject: Re: Circles and chords (Hint from author)
Message-ID: <1692@ihlpg.UUCP>
Date: Sat, 8-Mar-86 02:14:07 EST
Article-I.D.: ihlpg.1692
Posted: Sat Mar  8 02:14:07 1986
Date-Received: Sun, 9-Mar-86 00:13:29 EST
References: <965@h-sc1.UUCP> <2083@jhunix.UUCP> <974@h-sc1.UUCP>
Distribution: net
Organization: AT&T Bell Laboratories
Lines: 31

> The original puzzle: draw random chords of a circle of radius 2r,
> what percentage of them will intersect the concentric circle of
> radius r? (This is how it was posed to us)
> 
> > So depending upon which method we choose to generate random chords
> > we get an answer of 1/2, 1/3, or 1/4.  When stating that something
> > is to be chosen at random, it is important to state HOW it is to
> > be chosen at random. 
> > 
> >                                                         Dwight S. Wilson
> 
> I stand corrected. The problem was posed to us as intentionally ambiguous,
> but my real question for you puzzlers is to find as many different methods
> of drawing random chords that generate different percentages as you can.
> I found the above three solutions in the space of a few minutes,
> but after several hours of playing with the problem, I came up with two more,
> and another person in our seminar came up with still a sixth. It would be very
> interesting to see what others can come up with.
> 
>                                          - Tom Shields
>                                            Harvard University
----------------
All methods of choosing chords are random.  There are obviously an
uncountable infinity of percentages (all real numbers between zero
and one inclusive).  Perhaps you'd better place restrictions on
what you allow as a "good" random chord generator.
Remember, even a random number generator which returns the same number
every time is still a random number generator, even if it not a
very good one.
-- 
Bill Tanenbaum - AT&T Bell Labs - Naperville IL  ihnp4!ihlpg!tan