Apolitical Intelligence Tests With Important Point to Follow

Discussion in 'Political Opinions & Beliefs' started by ChemEngineer, Oct 8, 2019.

  1. roorooroo

    roorooroo Well-Known Member Past Donor

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    That is not the same problem as posed in the OP in my opinion. They are logically different. seems to me that the wiki problem "on a cue" means all 3 give their answer at the same time. The problem in the OP has the Prisoners giving their answers in order, P1 goes first, P2 goes second, P3 goes last. So P2 can use info deduced from P2's answer and P3 uses info from P1 and P2. It makes a difference. That is what I took from the Op's problem.

    Is this where our differences are coming from? An understanding of how the problem was intended?
     
  2. roorooroo

    roorooroo Well-Known Member Past Donor

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    Last edited: Oct 9, 2019
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  3. ChemEngineer

    ChemEngineer Banned

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    Corollaries continue to develop from my original point that even if everyone has the same information, some will misunderstand, others will spin and transmogrify the information so that they can come up with their own skewed positions. roorooroo has precisely nailed the point. Different problem, different solution.
    Some people don't pay enough attention, do they. Wanting to be right, or wanting others to be wrong really screws up the works.
     
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  4. FAW

    FAW Well-Known Member Past Donor

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    It is the same problem with one caveat that makes it easier, which is that the 3rd prisoner is not blind. Obviously any variant of this puzzle requires the answer of the other 2 or you dont have any form of a deductive reasoning brain teaser; you would just have 3 people guessing independently. Think this through.....

    When all 3 prisoners have black hats.....

    -Prisoner one sees 2 black hats and says I dont know. The range of possibilities is that he saw 2 black hats or one black and 1 red.

    --Prisoner 2 also sees 2 black hats. Since the range of possibilities that exist as a result of prisoner 1 saying he didnt know includes that P1 saw 2 black hats OR 1 of each, the fact that P2 saw 2 black hats leaves him the exact same problem that P1 had, which is that the range of possibilities is that P1 either saw one of each OR he saw 2 blacks, which leaves him in the exact same predicament as P1. He does not know.

    -P3 only knows that neither 1 or 2 both saw red hats. Beyond that, one or both could have seen 2 blacks OR 1 of each. If there were one red hat that P3 saw, then he could deduce with certainty. When there is 3 blacks however, there is not enough information. It is a probability problem.
     
    Last edited: Oct 9, 2019
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  5. ChemEngineer

    ChemEngineer Banned

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    Nigel's run-on sentence gives me brain ache:

    This is one of those problems that sort of gives you brain ache, (RUN-ON) you can work out the answer but explaining it clearly is more difficult...

    [It's also more difficult to write properly, Nigel.]
     
  6. roorooroo

    roorooroo Well-Known Member Past Donor

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    As I said:

    Concerning B B B

    there are actually two situations with BBB.... BBB and BBR. Because if the possibility of BBR didn't exist, P3 would know he is in black. So do you agree that both BBB and BBR need to be examined if we want to discuss BBB?

    So... BBR... P2 knows he is in black. Because if he was in red, P1 would have known he was in black.
    BBB... P1 and P2 don't know. There is the difference.

    If P1 and P2 don't know, P3 is in black.
    If P1 and/or P2 know, P3 is in red.
     
  7. FAW

    FAW Well-Known Member Past Donor

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    We are talking about 3 blacks. I get that when a red hat is on 1 or 2 that you can deduce with certainty.When there are 3 black hats , there is not enough information to deduce with certainty. You can only improve your odds, which happens to be EXACTLY what my link says.
     
    Last edited: Oct 9, 2019
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  8. roorooroo

    roorooroo Well-Known Member Past Donor

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    We cannot isolate the possibilities. It has to be considered logically as a whole. The seven possibilities serve to eliminate others.

    So once again:

    BBB

    if BBR is eliminated, P3 knows he is wearing black. We cannot isolate BBB from BBR. You said so yourself. If P1 and P2 are wearing black, you are saying that P3 may be in black or in red. Correct?
     
  9. roorooroo

    roorooroo Well-Known Member Past Donor

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    The following logic cannot be denied if P2 is privy to P1's answer and P3 is privy to P1 and P2's answers.

    ..................P1...........P2
    1. B B B unknown unknown
    2. B B R unknown black
    3. B R B unknown unknown
    4. B R R black ...... red
    5. R B B unknown unknown
    6. R B R unknown black
    7. R R B unknown unknown

    In the possibilities with P3 in black, neither P1 or P2 know their color. In the possibilities with P3 in red, either P1 or P2 or both will know their color. And that is what tells P3 whether he is black or red.

    The Wikipedia article has all 3 prisoners answering at the same time. Different than the OP.
     
  10. roorooroo

    roorooroo Well-Known Member Past Donor

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    Another problem analogous to the OP problem... the blind man is equivalent to the first man in line... he cannot see the other two men's hats.

    https://tierneylab.blogs.nytimes.com/2009/03/16/the-puzzle-of-the-3-hats/

    and another... again, the first man in line is analogous to the blind man

    https://www.popularmechanics.com/science/math/a24101/solution-to-riddle-of-the-week-5/

    and another:

    https://loveandlichen.wordpress.com...f-the-week-prisoners-dilemma-hats-not-econ-d/

    The OP's problem is all over the internet and it does have a definitive answer.
     
    Last edited: Oct 9, 2019
  11. FAW

    FAW Well-Known Member Past Donor

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    You introduce an interesting concept with the lack of BBR indicating BBB!! I think you are correct.



    Lets look at BBR

    -P1 sees 1 black and one red and says I dont know.
    -P2 sees red on P3 and black on P1. This tells P2 that his own hat is black since if his own hat was red, P1 would have seen 2 red hats. In that scenario the puzzle is over, because P2 the necessary information, which effectively eliminates BBR!

    Lets look at BBB

    -P1 sees 2 black hats, and correctly says "I dont know"

    -P2 also sees 2 black hats. P2 does not know if his hat is black or red, because the only thing he knows is that P1 either saw 2 blacks or 1 of each. P2 also says I dont know.

    -P3 sees nothing because he is blind. All he knows is that neither P1 or P2 saw 2 red hats. One or both P1 and P2 could be wearing black, but if number 3 had red, then number 2 would have known as in BBR which does in fact indicate that his hat is black!!

    I stand corrected ( I think). Well done. It is the ability to eliminate BBR that leads one to be able to detect BBB. I suppose that was included in the OP's original explanation. My bad.
     
    Last edited: Oct 9, 2019
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  12. roorooroo

    roorooroo Well-Known Member Past Donor

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    <big smile> Thank you for your effort. I was 99% certain I was right, but still had a small doubt. And I was also racking my brain trying to figure out a simple and direct way to show what I was thinking. Glad you see the logic! <big smile>
     
  13. rcfoolinca288

    rcfoolinca288 Well-Known Member Past Donor

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    You are still wrong. I met someone along the way does not mean at all they are going in a different direction. That is a fallacy.
     
  14. FAW

    FAW Well-Known Member Past Donor

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    LOL...in truth....there is still a very tiny doubt in my mind but I am pretty sure that you are right.
     
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  15. rcfoolinca288

    rcfoolinca288 Well-Known Member Past Donor

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    Roosters don't lay eggs.
     
  16. rcfoolinca288

    rcfoolinca288 Well-Known Member Past Donor

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    Your attempt at derailing your own thread with that link is pathetic.
     
  17. Phyxius

    Phyxius Well-Known Member

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    Or that the wives were even present. It only stated the man had seven wives, not that they were present at the time.
     
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  18. yguy

    yguy Well-Known Member

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    The inability to solve such problems is not even 1% of America's political problem. At least 99% of our problem is the apparent inability of so many people to recognize falsehoods which should be discernible as such by inspection, with no cogitation whatsoever.
    Since the speed is constant, all three points are equidistant, and one car is twice as fast as the other.
     
  19. rcfoolinca288

    rcfoolinca288 Well-Known Member Past Donor

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    --
     
    Last edited: Oct 10, 2019
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  20. Thedimon

    Thedimon Well-Known Member

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    Here is one easy one:
    You have 2 containers: 3 gallons and 5 gallons.
    You must obtain accurate 4 gallons of water.

    Here is a more complex one: 9+5=E. Explain what this math operation is about.
     
  21. roorooroo

    roorooroo Well-Known Member Past Donor

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    Fill up the five gallon container.
    Pour from the five gallon container to the three gallon container until it is full, leaving two gallons in the five gallon container.
    Empty the three gallon container.
    Pour the two gallons from the five gallon container into the three gallon container.
    Fill the five gallon container.
    Pour from the five gallon container into the three gallon container. Since the three gallon container already has two gallons in it, it will accept one gallon from the five gallon container, leaving four gallons in the five gallon container.
     
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  22. ChemEngineer

    ChemEngineer Banned

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    Correction. The solution may well be RBB. Prisoner #1 does not know if his is black or red. Prisoner #2 doesn't care. He is only concerned with red on Prisoner #3, irrespective of the hat color of Prisoner #1.
     
  23. FAW

    FAW Well-Known Member Past Donor

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    Agreed, although RBB was not in question as to being detectable. The only question left at that point in the conversation was whether or not BBB was detectable.
     
    Last edited: Oct 10, 2019
  24. Robert E Allen

    Robert E Allen Banned

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    1. the answer is one was going to st ives
    2 the answer is charcoal gray. The guard drew each hat, presumably with a pencil.. i guess you could call the hat white because he drew it on white paper and only has a pencil outline.
     
  25. ChemEngineer

    ChemEngineer Banned

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    "You have a truly dizzying intellect." - The Man In Black, in Princess Bride

    Oh, and "I am no one to be trifled with."
    "I'm not left-handed either."
     
    Last edited: Oct 10, 2019

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