Wason Card Puzzle

Published 28th Apr, 2009 | Philosophy | 68 Comments |

Ho ho! Today I have a fun little philosophical puzzle for you that you can impress your friends with (after getting it right yourself!) It’s called the Wason card problem, and only a reputed 5% of university-educated adults get it right!

If you are looking for the solution, you can find it here: Wason Card Puzzle Solution.

**********

There are four cards. On one side of each card is a number and on the other side is a letter, like so:

wason-card

The claim is:

“If a card has a vowel on one side, then it has an even number on the other side.”

The question is:

Which of the cards would one need to turn over to see if the claim is true or false?

See if you can get it (and no cheating!)

**********

After doing that one, try this one as well:

wason-cards2

Now, imagine you are a bartender. You must stop people under 21 years of age drinking alcohol. Each card above represents a person and shows their age on one side and what they are drinking on the other side. The claim is:

“If a person is drinking beer, then they are over 21 years of age.”

The question is:

Which of the cards do you need to turn over in order to check which people are breaking the law?

**********

Answers in the comments! ^_^

  • Philippe P.

    Errr, let’s guess…

    1) All vowels (to see they are even) and all odd numbers (to see they are not vowels) ?

    2) All sake-drinking cards (to see if they are of age), and all underage cards (to see if they are not having booze) ?

    This still makes a lot of cards to turn :)

  • Philippe P.

    Errr, let’s guess…

    1) All vowels (to see they are even) and all odd numbers (to see they are not vowels) ?

    2) All sake-drinking cards (to see if they are of age), and all underage cards (to see if they are not having booze) ?

    This still makes a lot of cards to turn :)

  • Ben

    The way you phrased it confused me at first (I thought you meant only flip ONE card), but the question may also be asked: “Which cards do you need to flip over to find out if the claim is false?”

    The answer:

    You need to turn the A and the 7. The claim says that if there’s a vowel on one side, there’s an even number on the other side, but not that the reverse must be true (an even number can be opposite a consonant as well). You turn the A to find out if the claim is basically true, then turn the 7 to make sure the other side isn’t a vowel since that’s the only one that could disprove the claim.

    The first reply is correct, but we only need to flip the cards in the example, so 2 cards in each case. The bar example makes things easier to understand.

    • http://gakuranman.com/ Mike

      Perfect reply! The reason the question is phrased as so is to avoid giving away too much information. If I said ‘which cards’ I immediately suggest that there is more than one to turn over :)

  • Ben

    The way you phrased it confused me at first (I thought you meant only flip ONE card), but the question may also be asked: “Which cards do you need to flip over to find out if the claim is false?”

    The answer:

    You need to turn the A and the 7. The claim says that if there’s a vowel on one side, there’s an even number on the other side, but not that the reverse must be true (an even number can be opposite a consonant as well). You turn the A to find out if the claim is basically true, then turn the 7 to make sure the other side isn’t a vowel since that’s the only one that could disprove the claim.

    The first reply is correct, but we only need to flip the cards in the example, so 2 cards in each case. The bar example makes things easier to understand.

    • http://gakuranman.com/ Mike

      Perfect reply! The reason the question is phrased as so is to avoid giving away too much information. If I said ‘which cards’ I immediately suggest that there is more than one to turn over :)

  • http://lostinkanjiland.blogspot.com/ Marisa

    A (it says all vowels map to even numbers but it doesn’t always follow that all even numbers will map to vowel so you don’t need to turn over the 4 as well)

    Beer and 17
    we do not know if the claim of over beer=>21 is true, and we have to check what the under 21year old is drinking. The soda or over 21 is unimportant.

  • http://lostinkanjiland.blogspot.com Marisa

    A (it says all vowels map to even numbers but it doesn’t always follow that all even numbers will map to vowel so you don’t need to turn over the 4 as well)

    Beer and 17
    we do not know if the claim of over beer=>21 is true, and we have to check what the under 21year old is drinking. The soda or over 21 is unimportant.

  • http://lostinkanjiland.blogspot.com/ Marisa

    oooh rereading it in the first one you would have to turn over 7 as well to check that wasn’t a vowel cause if it was the statement is incorrect.

    So please edit my answers to

    A+7
    Beer+17

  • http://lostinkanjiland.blogspot.com Marisa

    oooh rereading it in the first one you would have to turn over 7 as well to check that wasn’t a vowel cause if it was the statement is incorrect.

    So please edit my answers to

    A+7
    Beer+17

  • Kara

    My guess:

    On the first problem, you turn the 7 card to see if it has a vowel on the other side.
    On the second set, you turn the 17 card.

    It’s simpler to check for deviance than to confirm compliance.

    No college education. :)

  • Kara

    My guess:

    On the first problem, you turn the 7 card to see if it has a vowel on the other side.
    On the second set, you turn the 17 card.

    It’s simpler to check for deviance than to confirm compliance.

    No college education. :)

  • http://www.rockinginhakata.com/ Deas

    The question isn’t clear enough to justify Philippe’s approach, I think. The goal was not to disprove the rule, nor the scope of its accuracy, but to find if it’s true, apparently in only one direction, for the set of 4 cards we’re given. Right? So I’m guessing that we’d really only need to turn over the A card.

    The prompt: “If a card has a vowel on one side, then it has an even number on the other side.”

    The problem never suggests that the reverse of the prompt is true – that “if a card has an even number on one side it has a vowel on the other side.” So I say we don’t worry about it and just check the current proposition. Not set out to disprove or prove alternatives.

    I’m not so sure about the second question, though. Because we’re told that all cards are 2 sided, with the patron’s age on one side and their drink on the other, no less. Plus, we are given the imperative to halt underage drinking, I feel like it must be necessary to check both the Beer card and the 17 card. Safety first.

    Anyhoo – that’s my hazy early morning attempts at figuring it out. Am I close? Was Philippe right? :-)

    • http://gakuranman.com/ Mike

      Edited the statement for clarity. All cards are two-sided. Feel free to have another guess if you feel you need to ^^

      • http://www.rockinginhakata.com/ Deas

        Is this a philosophical game or a linguistic glitch game? I bet it’s all in how we read and interpret the question.

        By changing the first one to be clearer, both questions now have the same relationships, right? So I’ll stick with my Beer and 17 on the second one, but swap my first to A and 7. Seems to make sense to me.

  • http://www.rockinginhakata.com Deas

    The question isn’t clear enough to justify Philippe’s approach, I think. The goal was not to disprove the rule, nor the scope of its accuracy, but to find if it’s true, apparently in only one direction, for the set of 4 cards we’re given. Right? So I’m guessing that we’d really only need to turn over the A card.

    The prompt: “If a card has a vowel on one side, then it has an even number on the other side.”

    The problem never suggests that the reverse of the prompt is true – that “if a card has an even number on one side it has a vowel on the other side.” So I say we don’t worry about it and just check the current proposition. Not set out to disprove or prove alternatives.

    I’m not so sure about the second question, though. Because we’re told that all cards are 2 sided, with the patron’s age on one side and their drink on the other, no less. Plus, we are given the imperative to halt underage drinking, I feel like it must be necessary to check both the Beer card and the 17 card. Safety first.

    Anyhoo – that’s my hazy early morning attempts at figuring it out. Am I close? Was Philippe right? :-)

    • http://gakuranman.com/ Mike

      Edited the statement for clarity. All cards are two-sided. Feel free to have another guess if you feel you need to ^^

      • http://www.rockinginhakata.com Deas

        Is this a philosophical game or a linguistic glitch game? I bet it’s all in how we read and interpret the question.

        By changing the first one to be clearer, both questions now have the same relationships, right? So I’ll stick with my Beer and 17 on the second one, but swap my first to A and 7. Seems to make sense to me.

  • Kara

    And please edit to add that I don’t read the whole question….”which of the cards” could be plural……and the lack of the college education proves itself….

  • Kara

    And please edit to add that I don’t read the whole question….”which of the cards” could be plural……and the lack of the college education proves itself….

  • http://www.finalonline.co.uk/ Final

    Im struggling to even understand the question at the moment lol. Gunna have a go in the morning”^^

  • http://www.finalonline.co.uk Final

    Im struggling to even understand the question at the moment lol. Gunna have a go in the morning”^^

  • http://wrightak.blogspot.com/ Andrew

    Question 1: You would need to turn over A and 7. You need to turn over A because if there isn’t an even number on the back, then the statement is false. You need to turn over 7 because if there’s a vowel on the back then the statement is false.

    Question 2: Beer and 17. You need to turn over the beer because if it’s a minor on the other side then that person is breaking the law. You need to turn over 17 because if that person’s drinking alcohol, he/she’s breaking the law.

    It seems pretty simple to me. Am I making a dumb mistake somewhere? We only need to talk about the 8 cards in question right?

    • http://gakuranman.com/ Mike

      If it seems simple, wait until I post a harder puzzle of logic in the coming weeks :P Nice job and explanation by the way.

  • http://wrightak.blogspot.com Andrew

    Question 1: You would need to turn over A and 7. You need to turn over A because if there isn’t an even number on the back, then the statement is false. You need to turn over 7 because if there’s a vowel on the back then the statement is false.

    Question 2: Beer and 17. You need to turn over the beer because if it’s a minor on the other side then that person is breaking the law. You need to turn over 17 because if that person’s drinking alcohol, he/she’s breaking the law.

    It seems pretty simple to me. Am I making a dumb mistake somewhere? We only need to talk about the 8 cards in question right?

    • http://gakuranman.com/ Mike

      If it seems simple, wait until I post a harder puzzle of logic in the coming weeks :P Nice job and explanation by the way.

  • http://www.creeply.com/ kuroshirohaiir

    UHM!..Ocam’s razor that shit….you all are making it too complicated…you can flip over any card in either situation….by doing such you are either giving the claim one point or taking one point away. To get an absolute truth you would have to flip over all of the cards…

    none of you know philosophy….eeek -_-

  • http://www.creeply.com kuroshirohaiir

    UHM!..Ocam’s razor that shit….you all are making it too complicated…you can flip over any card in either situation….by doing such you are either giving the claim one point or taking one point away. To get an absolute truth you would have to flip over all of the cards…

    none of you know philosophy….eeek -_-

  • http://www.edufire.com/ Koichi

    I feel like this is one of those advertisements on the side of facebook. “How many triangles are there? Only 5% of college grads get this right” … I’m not even going to embarrass myself and try to figure this out. Not even going to bother finding a philosophical way around it. I’d just turn all the cards over – don’t know where this Wason guy gets this sort of cockiness.

    • http://www.creeply.com/ kuroshirohaiir

      I’m pretty sure he gets it from making Uni kids look dumb…in his time he was probably laughing by himself…..now mike is laughing at us

      • http://gakuranman.com/ Mike

        Actually, when I was still a wee first year Philosophy student and I was given this question, I got it wrong! oo;

        • http://www.creeply.com/ kuroshirohaiiro

          so what is the correct answer?

          • http://gakuranman.com/ Mike

            Wait another day or so and I’ll post it :p

  • http://www.edufire.com Koichi

    I feel like this is one of those advertisements on the side of facebook. “How many triangles are there? Only 5% of college grads get this right” … I’m not even going to embarrass myself and try to figure this out. Not even going to bother finding a philosophical way around it. I’d just turn all the cards over – don’t know where this Wason guy gets this sort of cockiness.

    • http://www.creeply.com kuroshirohaiir

      I’m pretty sure he gets it from making Uni kids look dumb…in his time he was probably laughing by himself…..now mike is laughing at us

      • http://gakuranman.com/ Mike

        Actually, when I was still a wee first year Philosophy student and I was given this question, I got it wrong! oo;

        • http://www.creeply.com kuroshirohaiiro

          so what is the correct answer?

          • http://gakuranman.com/ Mike

            Wait another day or so and I’ll post it :p

  • Biggi

    With the first task it’s A and 7. Because if the other card were turned, the “rule” that the cards with vows have even numbers could not be proven wrong with what may be on them whatsoever.

    So I assume that with the second one you should definetely skip the beer and 17 card because the soda is not of any interest as well as the 25 year old gal, ’cause he can drink whatever he wants.. ^-^ *grin*

  • Biggi

    With the first task it’s A and 7. Because if the other card were turned, the “rule” that the cards with vows have even numbers could not be proven wrong with what may be on them whatsoever.

    So I assume that with the second one you should definetely skip the beer and 17 card because the soda is not of any interest as well as the 25 year old gal, ’cause he can drink whatever he wants.. ^-^ *grin*

  • http://www.watermelonstudios.co.uk/ Satoshii

    I’m assuming you’d have to turn every card over, since even if you turn over all the vowels or even cards over, you’re still in the dark with the rest of them. It would support the claim, but it’s would necessarily prove it. Those cards having the vowel and the even number could just be coincidence. Any of those other cards could have either a vowel or even number on the back.

    C’mon, we need the answer! c)* v*)¬ 　・オ・ネ・ガ・イ・

  • http://www.watermelonstudios.co.uk Satoshii

    I’m assuming you’d have to turn every card over, since even if you turn over all the vowels or even cards over, you’re still in the dark with the rest of them. It would support the claim, but it’s would necessarily prove it. Those cards having the vowel and the even number could just be coincidence. Any of those other cards could have either a vowel or even number on the back.

    C’mon, we need the answer! \c)* v*)¬ 　・オ・ネ・ガ・イ・

  • Emily

    Ok, let’s think…
    The statement says only when there is a vowel, then the other side is an even number. It doesn’t say anything else. So I’ll flip over card A to see if it’s true. Because it doesn’t say that a consonant should NOT have a vowel too, so I don’t care about D and 7.
    So?

  • Emily

    Ok, let’s think…
    The statement says only when there is a vowel, then the other side is an even number. It doesn’t say anything else. So I’ll flip over card A to see if it’s true. Because it doesn’t say that a consonant should NOT have a vowel too, so I don’t care about D and 7.
    So?

  • Emily

    And for the latter, I’d turn the 17 card, to check if he’s drinking liquor, as he can’t be drinking beer ’cause anyone who drinks beer is in fact 21…
    So? SOSOSOSO????
    Give the friggin answer now!

  • Emily

    And for the latter, I’d turn the 17 card, to check if he’s drinking liquor, as he can’t be drinking beer ’cause anyone who drinks beer is in fact 21…
    So? SOSOSOSO????
    Give the friggin answer now!

  • http://divita.eu/ seifip

    A + 7
    Beer + 17

    :)

  • http://divita.eu Philip Seyfi

    A + 7
    Beer + 17

    :)

  • http://www.jamaipanese.com/ Jamaipanese

    I think my brain exploded -_-

  • http://www.jamaipanese.com Jamaipanese

    I think my brain exploded -_-

  • http://www.beta-guy.com/ Jeff

    I don’t know Philosophy, but the first one seem to be a simple logic question, with the statement, ‘all vowels have an even number on the other side’ then the question ‘Which of the cards would one need to turn over to see if the claim is true or false?’ the answer would be A as A is a vowel, you cannot assume to gain knowledge from any other card as odd numbers weren’t even spoken of so nothing can be verified from that, the even number may or may not have a vowel on the other side. it is possible to run into a statement that says all vowels have an even number on the other side, but not all even numbers have a vowel on the other side. As even numbers weren’t defined, only vowels.

    the next one seems simple enough you want to stop the 17 year old from drinking beer, so you flip the 17 card to see what the 17 year old is drinking. similar reasoning to the previous question. nothing can be learned from 25, soda and beer would not give you the full story, you want to select 17, as you want to see what he or she is drinking.

    All of that said, I can see no flaw with my answers but I am afraid I’m going to get it wrong, and there is a reasoned argument in favor of it. There seems to confusion from some of the posts about the purpose of the questions, only the 1 question is concerned about verifying the truth of the statement, the second one is only concerned with making sure the law isn’t broken. I don’t believe it is necessary to flip over multiple cards.

  • http://www.beta-guy.com/ Jeff

    I don’t know Philosophy, but the first one seem to be a simple logic question, with the statement, ‘all vowels have an even number on the other side’ then the question ‘Which of the cards would one need to turn over to see if the claim is true or false?’ the answer would be A as A is a vowel, you cannot assume to gain knowledge from any other card as odd numbers weren’t even spoken of so nothing can be verified from that, the even number may or may not have a vowel on the other side. it is possible to run into a statement that says all vowels have an even number on the other side, but not all even numbers have a vowel on the other side. As even numbers weren’t defined, only vowels.

    the next one seems simple enough you want to stop the 17 year old from drinking beer, so you flip the 17 card to see what the 17 year old is drinking. similar reasoning to the previous question. nothing can be learned from 25, soda and beer would not give you the full story, you want to select 17, as you want to see what he or she is drinking.

    All of that said, I can see no flaw with my answers but I am afraid I’m going to get it wrong, and there is a reasoned argument in favor of it. There seems to confusion from some of the posts about the purpose of the questions, only the 1 question is concerned about verifying the truth of the statement, the second one is only concerned with making sure the law isn’t broken. I don’t believe it is necessary to flip over multiple cards.

  • acidkun

    ok. this may sound stupid but i want to answer with different idea.

    for second one. i don’t need to turn over any card LOL
    the person who drinks soda and who is 25 is nothing to worry, right?

    what about the other two?
    the claim said “If a person is drinking beer, then they are over 21 years of age.”
    so the beer one is okay too.

    and why don’t i need to turn over 17 one. well because you said i’m bartender and i can see that this person is 17 so i wouldn’t sold him alcohol in the first place. :P

  • acidkun

    ok. this may sound stupid but i want to answer with different idea.

    for second one. i don’t need to turn over any card LOL
    the person who drinks soda and who is 25 is nothing to worry, right?

    what about the other two?
    the claim said “If a person is drinking beer, then they are over 21 years of age.”
    so the beer one is okay too.

    and why don’t i need to turn over 17 one. well because you said i’m bartender and i can see that this person is 17 so i wouldn’t sold him alcohol in the first place. :P

  • acidkun

    By the way, sorry for my lousy English.

    • http://gakuranman.com/ Mike

      Not at all! Your English is good! Thank you for taking part ^^

  • acidkun

    By the way, sorry for my lousy English.

    • http://gakuranman.com/ Mike

      Not at all! Your English is good! Thank you for taking part ^^

  • Pingback: Wason Card Puzzle Solution - Gakuranman

  • http://gakuranman.com/ Mike

    Alrighty then! Solution is here: http://gakuranman.com/wason-card-puzzle-solution/

    Well done to all! You all gave it a much better attempt than I did when I first tried this problem and got it wrong. Don’t feel bad if you got it wrong – learn from it and then put your cocky friends on the spot ;)

  • http://gakuranman.com/ Mike

    Alrighty then! Solution is here: http://gakuranman.com/wason-card-puzzle-solution/

    Well done to all! You all gave it a much better attempt than I did when I first tried this problem and got it wrong. Don’t feel bad if you got it wrong – learn from it and then put your cocky friends on the spot ;)

  • Tom Smith

    I disagree with your answer to the Watson Card puzzle. By turning the 7 card, you may have a chance to show that it is false, but if you do not find vowel, you do not know if the statement is true of false, which is what you are asked to prove. The A may still have a odd number under it.

    So there is no way to be certain by turning one card that you can prove it to be true or false.. All you can say is that you MAY prove it to be false, but you are just as likely to be unable to determine whether it is true or false with one card.

    On the other hand, the statement does not say “IF and only if you have a vowel, you will have an even number”, therefore whatever is on the other side of the 4 is not relevant, because whether it is a consonant of vowel will not determine true or false, and for the same reason D is not relevant.

    So you can only prove it either false or indeterminant by turning over the 7, and you can only prove it true or indeterminant by turning over the A.

    BTW, the reason why you can say that it is true if you turn over the A

  • Tom Smith

    I disagree with your answer to the Watson Card puzzle. By turning the 7 card, you may have a chance to show that it is false, but if you do not find vowel, you do not know if the statement is true of false, which is what you are asked to prove. The A may still have a odd number under it.

    So there is no way to be certain by turning one card that you can prove it to be true or false.. All you can say is that you MAY prove it to be false, but you are just as likely to be unable to determine whether it is true or false with one card.

    On the other hand, the statement does not say “IF and only if you have a vowel, you will have an even number”, therefore whatever is on the other side of the 4 is not relevant, because whether it is a consonant of vowel will not determine true or false, and for the same reason D is not relevant.

    So you can only prove it either false or indeterminant by turning over the 7, and you can only prove it true or indeterminant by turning over the A.

    BTW, the reason why you can say that it is true if you turn over the A

  • ndisi songa

    A AND 7

    i FEEL TO ANSWER THIS ONE HAS TO AFFIRM THE ANTECEDENT AND DENY THE CONSEQUENT

    tHE SECOND QUESTION'S ANSWER IS Sodfa and 25

  • ndisi songa

    A and 7
    Beer and 17

    In both of these cases, one has to affirm the antecedent and deny the consequent in order to verify the rule.

  • ndisi songa

    A and 7
    Beer and 17

    In both of these cases, one has to affirm the antecedent and deny the consequent in order to verify the rule.

  • Ndisi Songa

    I have visited this forum agai. Ok, i would turn over cards A and 7. By turning A, I want to confirm if the other side has an even number(confirming the antecedent) and I would also turn over card 7 to confirm the rule. If the other side has a vowel then the rule is not being followed.(denying the consequent).

  • Ndisi

    In the first question I would turn over cards A and card 7. Why these cards: Turning over card A would make me affirm whether the other side has an even number and card 7 to see if the other side really does not have a vowel. Hence, to test the rule one has to affirm the antecedent and deny the consequent.

    In the second question, i would have to interview the person drnking beer and the one who is 17 years old. By taking to the person who is drinking beer, i want to affirm the antecedent and am pnly denying the consequent by talking to the person who is under 21 yearsold in this case 17 years old.