Alrighty then! Time for the solution to that tricky little logic puzzle, the Wason Card Problem. I was impressed! I have many smart readers out there! (SPOILER)

In the hope of discouraging spoilers for people landing on this page, the answers are clearly published right at the very bottom of this post, but are included in the forthcoming explanation as to why the result is what it is. Go here and attempt the problem first. SPOILERS AHEAD

The Original Card Problem

The solution, to put it in philosophical terms, is (Social Psychology):

The only way to falsify an “if X, then Y” statement (“if vowel, then even number”) is by finding an instance of “X and not Y” (“vowel and odd number”). D and 4 are irrelevant, because these cards cannot combine a vowel and odd number.

What the heck does that mean? Basically, if order to show that the claim:

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

holds, we have to both verify it and test if for falsity. To verify it is true, you turn over the A card. If there is an even number, you know the claim to be true. But, we aren’t done. In order to make sure that the claim holds, we have to test the statement for falsity as well. This is the step most people don’t realise they must do.

Put simply, if I turned over the 7 card and found a vowel on the other side, it would mean that the claim is false. I must turn over the 7 card in order to check this, or I cannot be sure that my claim holds strong in all possible scenarios presented.

We do not need to check the D card, because it has no vowel and we are only talking about cards with vowels. There is no mention of what happens to consonants in the claim. We also do not need to turn over the 4 card, although it is very common for people to think there is a need to do so. I made this mistake and got the problem wrong when first presented with it a few years ago. Why, you ask?

The reason we don’t need to turn the 4 card over, is because our claim is not talking about what we find on the reverse side of even numbered cards. There could be pink ducks on the back of even numbered cards, for all we care. All we need to check is that there are no vowels paired up with odd numbered cards, because those sort of combinations are in direct conflict with our original claim. It says:

IF there was a VOWEL on one side, THEN it has an EVEN number on the other side.

It *does not* say that all even numbers must be paired with vowels. It *does not* say ‘if there is an even number on one side, then there is a vowel on the other side’. It only says that, if there is a vowel on one side, then there is an even number on the other side. Sounds strange? It is, but think about the beer problem below.

Supposedly the tendency to do want to check the 4 card has to do with confirmation bias (Skepdic):

I gave the Wason Card Problem to 100 students last semester and only seven got it right, which was about what was expected. There are various explanations for these results. One of the more common explanations is in terms of confirmation bias. This explanation is based on the fact that the majority of people think you must turn over cards A and 4, the vowel card and the even-number card. It is thought that those who would turn over these cards are thinking “I must turn over A to see if there is an even number on the other side and I must turn over the 4 to see if there is a vowel on the other side.” Such thinking supposedly indicates that one is trying to confirm the statement If a card has a vowel on one side, then it has an even number on the other side. Presumably, one is thinking that if the statement cannot be confirmed, it must be false. This explanation then leads to the question: Why do most people try to confirm a statement, when the task is to determine if it is false? One explanation is that people tend to try to fit individual cases into patterns or rules. The problem with this explanation is that in this case we are instructed to find cases that don’t fit the rule. Is there some sort of inherent resistance to such an activity? Are we so driven to fit individual cases to a rule that we can’t even follow a simple instruction to find cases that don’t fit the rule? Or, are we so driven that we tend to think that the best way to determine whether an instance does not fit a rule is to try to confirm it and if it can’t be confirmed then, and only then, do we consider that the rule might be wrong?

The Beer Card Problem

The beer problem is exactly the same as the original problem, although it is reputed more people get it right because it is easier to visualise and we can relate to the situation.

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

In the beer card problem, we first need to turn over the beer card. This is (hopefully) obvious because if the age on the reverse of the card was less than 21, the person would be breaking the law (i.e. invalidating the claim). The other card we need to turn over is the 17 card. This should seem more obvious than the previous example, because if the 17 year-old is drinking beer, they are breaking the law. We can’t know if they are breaking the law or not until we turn over the card.

We do not need to turn over the soda card because it isn’t alcohol – anyone, both under and over 21 can drink it. We also do not need to turn over the 25 card because adults can drink soft drinks as well as alcohol – there is no need to check what the person who is of legal age is drinking.

If you were having trouble seeing why we turned over the A and 7 in the previous problem, try relating the two problems again and see if it makes it clearer ^^.

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Answer to the vowels and numbers card problem:

You need to turn over cards A and 7

Answer to the drinks and ages card problem:

You need to turn over cards beer and 17

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Well done to all those who got it right! I will be posting a couple more problems like this in the coming weeks which I found interesting. They are very satisfying to solve if you put in the time to sit and think about them for a little while! ^^ If you got it wrong – don’t worry. Learn from it and become wiser :D

More info here: Skeptic Wiki