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Which Twin is Telling the Truth?

Date: 3/2/96 at 9:35:34
From: sarahd
Subject: which twin is telling the truth?

This is more of an English question, but it is in my math book:

A man is walking to a party. There is a fork in the road.
He doesn't know which way to go.  At the fork in the road are 
identical twins.  One always lies and One always tells the truth, 
but you don't know who tells what. If you can only ask one 
question (the same question to each twin), what is it?


Why would you ask that: 


Date: 3/4/96 at 21:39:51
From: Doctor Ken
Subject: Re: which twin is telling the truth?

Hello there!

Actually, I'd say that this question is a perfectly good math question, 
in the part of math called Logic (some people do like to think of 
Logic as a field of Philosophy, though).

Anyway, what's true about this question is that you actually only 
need to ask _one_ of the twins your question, you don't even need 
to ask both of them.  You'll get enough information from one to 
make your decision.  

Let me give you a couple of hints, and then see whether you can 
take it from there.  

Since you don't know which twin you're talking to, it seems 
like you're not going to be able to tell whether your answerer is 
lying or telling the truth, and therefore whether the answer is 
true or false.  It seems to be a lost cause.


You actually _can_ solve this problem!  Try to get the guy you 
ask to incorporate what the _other_ guy would say to your question.  
Then, if that works, try to figure out why (I mean, think about the 
problem even after you solve it).  

Good luck!

[See also the Classic Problem "Liars and Truthtellers" in the
Dr. Math FAQ:   .]

-Doctor Ken,  The Math Forum

Associated Topics:
High School Logic
Middle School Logic

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