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Which Chair you will choose ?


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30 replies to this topic

#21 MikeD

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Posted 28 June 2012 - 07:06 AM

Spoiler for now that I had time

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#22 MikeD

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Posted 28 June 2012 - 07:09 AM

@bushindo I like you answer. :thumbsup:
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#23 bonanova

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Posted 28 June 2012 - 07:26 AM

Hi MikeD. We seem to be converging on a solution.
I think we differ only in one case: mmb.


See previous post for my analysis of that case.
See comment in red inside your spoiler for a question about yours.

Thanks. :)

Spoiler for now that I had time


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

#24 MikeD

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Posted 28 June 2012 - 07:39 AM

Hope this helps, I sometimes have a hard time explaining things.

Spoiler for reasoning

Edited by MikeD, 28 June 2012 - 07:40 AM.

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#25 bushindo

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Posted 28 June 2012 - 07:47 AM

Spoiler for now that I had time


Nice work! I think you have the correct answer.


This is a nice analysis to maximize probability that your answer is correct. I had understood the puzzle to require that when you answer you must be certain that your answer is correct. Then, each chair gives you a particular probability of being the first to be able to answer with certainty of your color.

If the student cannot logically deduce the colors, she will move on to the second chair, then the third chair. If that does not decide the issue, she will continue around the circle of chairs until one of you gives the correct response, with correct reasoning, based on the stamps that are visible and the other students' answers.


That was an attempt to think outside the box. It definitely doesn't fit the constraint of the OP unless we considerably relax the definition of 'logically deduce' ^_^

Edited by bushindo, 28 June 2012 - 07:49 AM.

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#26 bonanova

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Posted 28 June 2012 - 08:01 AM

Hope this helps, I sometimes have a hard time explaining things.

Spoiler for reasoning


You explained it well; I just was slow to follow it. ;)

Spoiler for I agree

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

#27 Godsryche

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Posted 03 July 2012 - 09:23 PM

With this being a Logic class, perhaps we don't need to do any math at all...

Spoiler for No Math

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#28 bonanova

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Posted 05 July 2012 - 06:26 AM

With this being a Logic class, perhaps we don't need to do any math at all...

Spoiler for No Math


The difficulty with this approach is that if the students do as the OP requires, the student who made your additional assumption of fairness would pick chair #2. :(

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#29 MikeD

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Posted 05 July 2012 - 10:58 AM

I think though that for fairness the teacher would randomly assign the stamps. If she chose the order of stamps, she would be favouring a chair and therefore a student. For example, if she chose 1 black one and 1 white one for each student, then she would be favouring the student in the second chair.
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#30 Godsryche

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Posted 05 July 2012 - 12:36 PM

The difficulty with this approach is that if the students do as the OP requires, the student who made your additional assumption of fairness would pick chair #2. :(


But the student in the first chair gets to guess first, no? So, if I walk in with the fairness assumption, then I don't really even need to see what the other two students have on their heads in order to determine what mine are.
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