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### Who is a Liar, Who Tells the Truth?

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Date: 9/4/96 at 19:7:34
From: Anonymous
Subject: Who is a Liar, who Tells the Truth

The inhabitants of a certain island have a strange characteristic:
those who are swimmers always tell the truth, and those who are non-
swimmers always lie.

You visit the island and meet a group of three native inhabitants.
You ask the first person, "Are you a swimmer?" The answer is
unintelligible. The second person immediately says, "That was 'yes.'
I am a swimmer, too." The third person says, "They are both lying."

Is each of these three people a swimmer or a nonswimmer?

My answer: The first is a nonswimmer, the second is also a nonswimmer,
the third one is a swimmer.
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Date: 9/4/96 at 21:54:41
From: Doctor Robert
Subject: Re: Who is a Liar, who Tells the Truth

Put yourself in the place of the second of the three natives.  If the
first person is a swimmer he will say "I am a swimmer."  If the
first person is a non-swimmer, he will also say "I am a swimmer"
(because he always lies).  So, the thing that the second person hears
is "I am a swimmer."

When the second person says that the first person says he is a
swimmer, the second person is telling the truth and is therefore a
swimmer.

Now, the third person says that the second person is lying - which is
wrong.  So that makes the third person a non-swimmer.  Unfortunately,
we do not know whether the first person is a swimmer or non-swimmer.
Using S for swimmer and N for non-swimmer, the possibilities are

SSN   or NSN

Dr. Math FAQ:

http://mathforum.org/dr.math/faq/faq.liar.html   .]

-Doctor Robert,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Logic

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