You see four cards with A, D, 3, and 6 face-up. You know that each card has a letter on one side and a number on the other side.

You are told that cards with a vowel on one side must have an even number on the other side. Which cards do you need to turn over to test if this rule is broken?

#### Solution

A and 3

It’s obvious that you need to turn over the “A” card to check whether it has an even number on the other side.

You need to turn over the “3” card to check whether it has a vowel on the other side (because if it did have a vowel on the other side, not having an even number on this side breaks the rule).

You do NOT need to turn over the “6” card, because the rule does NOT say that a card with an even number on one side must have a vowel on the other side (only the other way around).

#### More about this puzzle

The four-card problem (also known as the four-card task or the Wason selection task) is a classic logical reasoning puzzle. Psychologists found that people answer this correctly more often when the problem is framed in a real-world context.

For example, you have cards that show the age of a person one side and what they are drinking on the other side. Let’s say you are shown four cards that have on one side: person drinking coke, person drinking beer, 16-year old, 22-year old. If you are told that people drinking beer must be over 18, you might have an easier time determining which cards need to be turned over than in the puzzle above.

Don’t you need to check the D card too? It could have a vowel on the other side. The set-up doesn’t seem to rule out that possiblity.

Fair enough. The assumption is that every card has a number on one side and a letter on the other side, but you’re right that this was not spelled out. The question has been revised to state this. Good catch!