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Subject: "A Riddle"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #425
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idavis1
Member since Feb-17-04
Feb-17-04, 02:20 PM (EST)
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"A Riddle"
 
   My logic teacher gave our class a riddle and normally I don't care much for riddles but I was perplexed and have been tihnnking constantly about it. Everyone seems to know the answer except for me.
It goes something like this:
There are identical twins. One's name is Jon. One always lies and one always tells the truth.
I have to ask one of the brothers one 3 word question to find out both who's jon and who's the liar.
Any genius's out there who can figure this out, I certainly could not.:7


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  Subject     Author     Message Date     ID  
A Riddle idavis1 Feb-17-04 TOP
  RE: A Riddle alexb Feb-17-04 1
     RE: A Riddle Ramsey_KJ Dec-04-04 7
     RE: A Riddle Graham C Dec-11-04 9
         RE: A Riddle Graham C Dec-11-04 11
  RE: A Riddle idavis1 Feb-19-04 2
     RE: A Riddle alexb Feb-19-04 3
  RE: A Riddle Don Apr-02-04 4
  RE: A Riddle schizophoenix Apr-04-04 5
     RE: A Riddle quintopia Dec-03-04 6
  RE: A Riddle sexymathsman Dec-10-04 8
     RE: A Riddle rewboss Dec-11-04 10
         RE: A Riddle Bigboss Jan-08-05 12
             RE: A Riddle Ramsey_KJ Jan-09-05 13
                 RE: A Riddle Bigboss Jan-09-05 14
                     RE: A Riddle Graham C Jan-10-05 15
                         RE: A Riddle Bigboss Jan-10-05 16
                             RE: A Riddle Graham C Jan-11-05 17
                                 RE: A Riddle Bigboss Jan-12-05 18
                                     RE: A Riddle Ramsey_KJ Jan-12-05 20
                                 RE: A Riddle rewboss Jan-12-05 19
                                     RE: A Riddle Bigboss Jan-13-05 21
                                         RE: A Riddle rewboss Jan-14-05 22
                                         RE: A Riddle Graham C Jan-14-05 23
                                             RE: A Riddle Bigboss Jan-14-05 24
  RE: A Riddle brenteknik 27 Jan-18-05 25
     RE: A Riddle Ramsey2879 Jan-19-05 26
     RE: A Riddle rewboss Jan-20-05 27
     RE: A Riddle xalias Jan-20-05 28
     RE: A Riddle Bigboss Jan-24-05 29
         RE: A Riddle seraphx Jan-25-05 30
             RE: A Riddle Bigboss Jan-26-05 31
  RE: A Riddle NR Jan-27-05 32
     RE: A Riddle Pierre Charland May-26-08 34
  RE: A Riddle teclis May-15-08 33

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alexb
Charter Member
2228 posts
Feb-17-04, 02:38 PM (EST)
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1. "RE: A Riddle"
In response to message #0
 
   >There are identical twins. One's name is Jon. One always
>lies and one always tells the truth.

So they are not quite identical.

>I have to ask one of the brothers one 3 word question to
>find out both who's jon and who's the liar.

I am pretty sure that there is no such question. On the other hand, there is a 3 word question whose answer reveals who is Jon; and there is another 3 word question whose answer reveals who is the liar.

(But you must stipulate that only one of the brothers is Jon.)

>Any genius's out there who can figure this out, I certainly
>could not.:7

This puzzles appears on pp. 42-44 of R. Smullyan's 5000 B.C. and Other Philosophical Fantasies.

>Everyone seems to know the answer except for me.

This is probably because they read the book. Why do not you?

As a hint, the two questions mentioned above have the property that when you ask either one of the questions you can find a correct answer to the other.


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Ramsey_KJ
Member since Sep-23-04
Dec-04-04, 08:43 PM (EST)
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7. "RE: A Riddle"
In response to message #1
 
   I don't have time to check but could the questions be something like ask one twin "Are you Jon" then ask the other twin "Am I Here".
Have a Good Day
KJ Ramsey


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Graham C
Member since Feb-5-03
Dec-11-04, 07:41 AM (EST)
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9. "RE: A Riddle"
In response to message #1
 
   >
>I am pretty sure that there is no such question.

Isn't one way of envisaging this:

Make a table showing the answer you get.

if the___________If you picked
liar is________Jon______the other
Jon___________?__________?
the other______?__________?

To satisfy both questions you must one cell must be different from the other three. But a single question can only distinguish between the rows OR the columns.

Thus 'Are you Jon?' gives

if the___________If you picked
liar is________Jon______the other
Jon___________No__________No
the other_____Yes_________Yes

'Does Jon lie?' gives

if the___________If you picked
liar is________Jon______the other
Jon___________No__________Yes
the other______No__________Yes

and so on.


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Graham C
Member since Feb-5-03
Dec-11-04, 10:36 AM (EST)
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11. "RE: A Riddle"
In response to message #9
 
   I should have added:

If you ask both questions in succession then you get four combinations.
No,no - you picked Jon and Jon is the liar
No,yes - you did not pick Jon, and Jon is the liar
Yes,no - you picked Jon, but Jon is not the liar
Yes,yes - you did not pick Jon and Jon is not the liar

Or, as a table

if the_____________If you picked
liar is__________Jon________the other
Jon___________No,No_______No,Yes
the other______Yes,No_______No,No


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idavis1
guest
Feb-19-04, 11:46 AM (EST)
 
2. "RE: A Riddle"
In response to message #0
 
   I figured out the question. It would be Does Jon Lie?
Yeah only took me a whole week


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alexb
Charter Member
2228 posts
Feb-19-04, 11:49 AM (EST)
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3. "RE: A Riddle"
In response to message #2
 
   >I figured out the question. It would be Does Jon Lie?

If you are interested in who is Jon, that's the question.
However, if you are concerned with whether Jon is a liar, you should look for another question.

>Yeah only took me a whole week

You did eat, did not you?


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Don
guest
Apr-02-04, 11:18 PM (EST)
 
4. "RE: A Riddle"
In response to message #0
 
   'Course, assuming Jon isn't some sort of solipsist or somesuch, the question "Am I here?" ought to provide another good indicator.


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schizophoenix
Member since Jan-14-04
Apr-04-04, 01:43 PM (EST)
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5. "RE: A Riddle"
In response to message #0
 
   just a thought - i think the best you can do here is to ask "jon, am i?"

if you get a response you know both who jon is and who the liar is. if you do not get a response you know who jon is =)

am i cheating?


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quintopia
guest
Dec-03-04, 06:29 PM (EST)
 
6. "RE: A Riddle"
In response to message #5
 
   schizophoenix: Your method will not work. If Jon is the liar, answering would reveal that he is Jon. Because he is a liar, he will not say anything to avoid admitting this. Thus, you will receive no answer, and will not know the answer to either question.


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sexymathsman
guest
Dec-10-04, 01:27 PM (EST)
 
8. "RE: A Riddle"
In response to message #0
 
   i know what it is. the question would be does john lie?


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rewboss
guest
Dec-11-04, 07:41 AM (EST)
 
10. "RE: A Riddle"
In response to message #8
 
   >i know what it is. the question would be does john lie?

That will only tell you if the person you are addressing is Jon or not, but not the identity of the liar.

Any question with a yes/no answer won't work, because there are only two possible answers -- but we have four combinations to work with. Calling the twins A and B, the combinations are:

A is Jon, A is the liar
A is Jon, B is the liar
B is Jon, A is the liar
B is Jon, B is the liar

Whatever question it is, it has to be open-ended.


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Bigboss
guest
Jan-08-05, 09:09 PM (EST)
 
12. "RE: A Riddle"
In response to message #10
 
   "You twins, Jon?"

Possible answers
Yes
Yes, but my name isn't Jon
No
No and my name isn't Jon


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Ramsey_KJ
Member since Sep-23-04
Jan-09-05, 08:18 AM (EST)
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13. "RE: A Riddle"
In response to message #12
 
   >"You twins, Jon?"
>
>Possible answers
>Yes
>Yes, but my name isn't Jon
>No
>No and my name isn't Jon

How about the answer "My name isn't Jon"

Have a Good Day
KJ Ramsey


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Bigboss
guest
Jan-09-05, 11:57 PM (EST)
 
14. "RE: A Riddle"
In response to message #13
 
   How about no answer at all?
What if they are partially deaf, or do not respond to a certain range of frequencies?
How about replying to the question only if they think you were polite enough?

You ask the twin a single question to derive 2 elements, identity and disposition towards the truth. No question can "force" them to address both elements.


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Graham C
Member since Feb-5-03
Jan-10-05, 01:57 PM (EST)
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15. "RE: A Riddle"
In response to message #14
 
   'You twins, Jon?' is two questions, not one.


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Bigboss
guest
Jan-10-05, 09:18 PM (EST)
 
16. "RE: A Riddle"
In response to message #15
 
   "You twins, Jon?" is a single question, in the same way "You are twins, Jon" is a single sentence. The matter of it engaging 2 elements is different.


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Graham C
Member since Feb-5-03
Jan-11-05, 04:22 PM (EST)
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17. "RE: A Riddle"
In response to message #16
 
   >"You twins, Jon?" is a single question, in the same way "You
>are twins, Jon" is a single sentence. The matter of it
>engaging 2 elements is different.

It's not actually a sentence at all. Nor, formally, is it a question. If it were one sentence, that wouldn't mean it was one question: it's quite easy to formulate several questions in one sentence.

Moreover it doesn't work anyway. If you happen to ask the liar and he says 'No, and my name is Fred' - which is likely - where are you? You know he's the liar, and his name therefore is not Fred, but that doesn't prove it is or isn't Jon.


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Bigboss
guest
Jan-12-05, 08:14 AM (EST)
 
18. "RE: A Riddle"
In response to message #17
 
   I was mistaken. I apologise for my earlier condunct.


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Ramsey_KJ
Member since Sep-23-04
Jan-12-05, 10:29 PM (EST)
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20. "RE: A Riddle"
In response to message #18
 
   I think no apologies are necessary. In fact if any one three word question would work, yours would also. Thanks for the fresh insight. Note that according to Alex, there are two questions to be posed not one. But your question stands a fair chance of eliciting all the necessary information by itself.
Have a Good Day
KJ Ramsey


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rewboss
guest
Jan-12-05, 08:14 AM (EST)
 
19. "RE: A Riddle"
In response to message #17
 
   In fact, it is both a question and a sentence. Just because it ha