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Identical twins, sort of


Best Answer Rainman, 16 January 2014 - 04:58 PM

Spoiler for

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#1 bonanova

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Posted 26 December 2013 - 08:02 AM

Identical twins Cal and Hal look alike, act alike and seem to talk alike. If asked whether 2+2=5, both would say No. "Is the sky blue?" would get a Yes from them both. Yet one always tells the truth, while the other always lies. That is because the truthteller has an accurate view of the world, and truthfully presents it, while the liar has a totally inaccurate world view (he believes the sky is not blue) and wrongfully presents that view. Thus they will give the same response to the same question.

Joe and Moe, themselves twins and also logicians of some repute, pondered this strange behavior one day. They wondered: if they were to meet one of the two brothers alone, would it be possible, by asking him any number of yes-no questions, to find out which one he is? Joe said, "No, it would not be possible because whatever answers you got to your questions, the other brother would have given the same answers." Moe claimed that it was possible to find out. Moe was right, and the puzzle has two parts: (1) How many questions are necessary?; and (2) more interesting yet, What was wrong with Joe's argument?


- Puzzle due to R. Smullyan.
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#2 the_count

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Posted 27 December 2013 - 01:02 AM

Might be able to do it with one question like...

 

Spoiler for Identical twins, sort of


Edited by the_count, 27 December 2013 - 01:11 AM.

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#3 bonanova

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Posted 27 December 2013 - 06:21 AM

Might be able to do it with one question like...
 

Spoiler for Identical twins, sort of



Hi Count, and welcome to the Den.
Your question solves the first part of the puzzle.
To answer the second part, think of some other questions and determine what they have in common.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 the_count

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Posted 27 December 2013 - 10:05 AM

Thanks for the warm welcome bonanova...I shall ponder your hints further :)


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#5 Unraveler

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Posted 14 January 2014 - 06:05 PM

The same question but in reverse; are you a truthteller. I think that would produce the same result.


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#6 Nins_Leprechaun

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Posted 15 January 2014 - 01:50 AM

Hopefully this should answer the second question
Spoiler for

Edited by Nins_Leprechaun, 15 January 2014 - 01:52 AM.

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#7 Rainman

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Posted 16 January 2014 - 04:58 PM   Best Answer

Spoiler for


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#8 bonanova

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Posted 25 January 2014 - 05:27 AM

Spoiler for

 

Spoiler for Rainman has it


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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