# Logical puzzle

## It is necessary to turn over: (multiple answers are allowed)

1. Apr 7, 2016

### micromass

Staff Emeritus
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:

Card 2:

Card 3:

Card 4:

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2. Apr 7, 2016

### ProfuselyQuarky

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

3. Apr 7, 2016

### 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.

4. Apr 7, 2016

### ProfuselyQuarky

3 can hardly be considered a worthy sample size, though :)

5. Apr 7, 2016

### 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).

6. Apr 7, 2016

### micromass

Staff Emeritus
Never mind that PF has a special audience. On the site they linked, they do get numbers like 75%-80% get it wrong.

7. Apr 7, 2016

### ProfuselyQuarky

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
8. Apr 7, 2016

### zoobyshoe

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.

9. Apr 7, 2016

### micromass

Staff Emeritus
Why turn over card 3?

10. Apr 7, 2016

### Staff: Mentor

How could card 3 violate the rule? Which shape would lead to a violation?

11. Apr 7, 2016

### zoobyshoe

Yes, you're right.

12. Apr 7, 2016

### 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".

13. Apr 7, 2016

### micromass

Staff Emeritus
Indeed. I have used this example to explain the truth table of $P\Rightarrow Q$ to new students. It worked perfectly.

14. Apr 7, 2016

### 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.

15. Apr 7, 2016

### SophiaSimon

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.

16. Apr 7, 2016

### Psinter

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 $p\rightarrow q$ we can conclude that $q\rightarrow p$. But I remember in a course a professor asking a question like that and his answer was: We cannot conclude that $q\rightarrow p$ just because $p\rightarrow q$. 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
17. Apr 8, 2016

### Enigman

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"

18. Apr 8, 2016

### reenmachine

$P \rightarrow Q$ 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.

19. Apr 8, 2016

### 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.

20. Apr 8, 2016

### PeroK

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.