Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Logical puzzle

  1. Card 1

  2. Card 2

  3. Card 3

  4. Card 4

Multiple votes are allowed.
Results are only viewable after voting.
  1. Apr 7, 2016 #1

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The recent thread of @ProfuselyQuarky reminded me of this fun puzzle. It's called the Wason's Selection Test. I stole it pretty obviously from the following website, so do check it out: http://www.philosophyexperiments.com/wason/ About 75%-80% get this wrong.

    You are a quality control technician working for a card games manufacturer. You have to ensure that cards have been produced in accordance with the following rule:

    If a card has a circle on one side, then it has the colour yellow on the other side.


    You already know for certain that every card has a shape on one side and a colour on the other side. Please indicate, taking this into account, which card or cards you definitely need to turn over, and only that or those cards, in order to determine whether the rule is broken in the case of each of the four cards below.

    Card 1:
    square.gif

    Card 2:
    circle.gif

    Card 3:
    yellow.gif

    Card 4:
    red.gif
     

    Attached Files:

  2. jcsd
  3. Apr 7, 2016 #2

    ProfuselyQuarky

    User Avatar
    Gold Member
    2016 Award

    I never saw this one before, micromass, but I really like it . . .

    Well, I'll see if I feel the same way once we're officially told the correct answer :smile:
     
  4. Apr 7, 2016 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    3 correct answers so far and 0 wrong answers. We can exclude the hypothesis "at least 75% get it wrong" with p<0.02, but physicsforums users are not representative, so it should not be surprising.
     
  5. Apr 7, 2016 #4

    ProfuselyQuarky

    User Avatar
    Gold Member
    2016 Award

    3 can hardly be considered a worthy sample size, though :)
     
  6. Apr 7, 2016 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    So what? You can discover something new with a single event, if it is significant enough.
    Now 4:1 (with some assumption about votes, because now it is not obvious any more).
     
  7. Apr 7, 2016 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Never mind that PF has a special audience. On the site they linked, they do get numbers like 75%-80% get it wrong.
     
  8. Apr 7, 2016 #7

    ProfuselyQuarky

    User Avatar
    Gold Member
    2016 Award

    Okay, fine. I didn't click the link (and I kind of/sort of just jumped to the puzzle, too, without reading the first sentences of your post).
     
    Last edited: Apr 7, 2016
  9. Apr 7, 2016 #8
    I think you have to turn over cards 2, 3 and 4.

    #1 has a square showing, but there's no rule about squares to check.

    Cards 2 and 3 have to be checked for obvious reasons, but card 4 also has to be checked to make sure there's no circle on the reverse.
     
  10. Apr 7, 2016 #9

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Why turn over card 3?
     
  11. Apr 7, 2016 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    How could card 3 violate the rule? Which shape would lead to a violation?
     
  12. Apr 7, 2016 #11
    Yes, you're right.
     
  13. Apr 7, 2016 #12

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I checked the linked website. They have a variant with alcoholic drinks (question 3 of 3), and there the fraction that gets it right is significantly larger: "I don't have to check what the 22-year-old drinks, but I have to check what the 17-year-old drinks".
     
  14. Apr 7, 2016 #13

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Indeed. I have used this example to explain the truth table of ##P\Rightarrow Q## to new students. It worked perfectly.
     
  15. Apr 7, 2016 #14

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That one is quite interesting as well.
    One word of warning: If the conclusion is "therefore, some [foo] are [bar]", they only consider this as valid conclusion if you know for sure that some [foo] exist. The English language is not precise enough for that.
     
  16. Apr 7, 2016 #15
    Ahh, I was initially wrong. I picked 2, 3, and 4. But you don't have to check 3. That bright yellow got my attention and I ran with it, tricky, tricky.
     
  17. Apr 7, 2016 #16
    I see when you guys post these puzzles and tell myself that I don't care, but then you post the phrases x% or y% of people get it wrong. Because I don't want to be with the wrong side I stay and solve it only to discover I got it wrong, get mad, and leave the forum.
    That's until Psinter comes and gets it wrong.

    Anyway, can someone explain the following to me and tell me whether I'm getting it wrong? The websites says that since [itex]p\rightarrow q[/itex] we can conclude that [itex]q\rightarrow p[/itex]. But I remember in a course a professor asking a question like that and his answer was: We cannot conclude that [itex]q\rightarrow p[/itex] just because [itex]p\rightarrow q[/itex]. Yet the answer to this puzzle says that we can do that. How come? Am I wrong? I think the puzzle answer is wrong.

    Edit: I found this: https://en.wikipedia.org/wiki/Affirming_the_consequent

    According to that, one answer of the puzzle, according to the website, is wrong. Because it is affirming the consequent. I think. Someone correct me if I'm wrong.
    It says: If a card has a circle on one side, then it has the colour yellow on the other side.

    Then it says that because it has yellow, it must have a circle on the other side. That's affirming the consequent, you don't know whether your statement will be true.
     
    Last edited: Apr 7, 2016
  18. Apr 8, 2016 #17
    What the website actually says is :
    People almost always recognise that they have to turn over the card with the circle (P), but they fail to see that they also have to turn over the card with the colour red (not-Q). It is also common for people to think - mistakenly - that they have to turn over the card with the colour yellow (Q).
    You don't have to turn over the yellow card because it doesn't matter if it has a circle on the other side or a square. The rule is "P implies Q" and not "if and only if P then Q"
     
  19. Apr 8, 2016 #18

    reenmachine

    User Avatar
    Gold Member

    ##P \rightarrow Q## doesn't have the same truth table as ##Q \rightarrow P##, but it does in the case of ##\neg Q \rightarrow \neg P##.

    So what you have to do is flip the card when the premise of either ##P \rightarrow Q## or ##\neg Q \rightarrow \neg P## is true to see if the conclusion is false, because that's when the rule is broken.
     
  20. Apr 8, 2016 #19

    Borek

    User Avatar

    Staff: Mentor

    @micromass - I think you skewed the result by referring to the ProfuselyQuarky post. Everyone who has seen the other thread thinks twice before answering here.
     
  21. Apr 8, 2016 #20

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    And in the general population there would not necessarily be a clear understanding of precisely what the rule means.

    It would be easy to interpret the rule (in an everyday use of the word "if") to mean that circle and yellow go together. In logical terms to interpret "if" as "if and only if". It's only doing maths or computer programming that leads to a concrete interpretation of something like this.

    With the drinking example, the everyday context excludes the "if and only if" interpretation. People naturally interpret this example as "if".

    This is perhaps as much about language interpretation than logic.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Logical puzzle
  1. Logic puzzle (Replies: 173)

  2. A Logic Puzzle (Replies: 10)

  3. Logic Puzzles (Replies: 4)

  4. Logic Puzzles (Replies: 0)

Loading...