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### Logic - Liars & Truthtellers (What Question Does She Ask?)

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Date: 12 Mar 1995 00:21:59 -0500
From: Anonymous
Subject: Another Math Question

A logician vacationing in the South Seas finds herself on an
island inhabited by the two proverbial tribes of liars and
truth-tellers. The members of one tribe always tell the truth,
and the members of the other always lie.  She comes to a fork
in the road and has to ask a native bystander which path she
should take to reach a village.  She has no way of telling
whether the native is a liar or a truth-teller.  To further
complicate matters, the natives of the island will only answer
yes-or-no questions. The logician thinks a moment, then asks
take.  What question does she ask?

Thanks a whole lot!
```

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Date: 12 Mar 1995 12:44:31 -0500
From: Dr. Ethan
Subject: Re: Another Math Question

Hello!

The key here is to ensure that you phrase the question so that
you will get the same answer from both parties.  To do this, you
need to ask a question that will involve both of their opinions.

The liar will say no, the truth teller yes.

But what if I ask this question:  "If I were to ask a member of the
tribe that you don't belong to 'Is water wet?' what would he say?"

Well, the truth teller would answer truthfully that the liars would
lie and say no.  The liar would lie and say that the truth tellers
would say no.

So you see with this new way that we have phrased the question,
we have guaranteed a falsehood, so the opposite must be true.
Think how you might phrase a question related to your problem in
a similar way.

Good Luck.

Dr. Math FAQ:

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

Ethan, Doctor On Call
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Associated Topics:
High School Logic
High School Puzzles

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