Four Cards, One Rule

Each card has a letter on one side and a number on the other. You see A, K, 4 and 7. The rule says: if a card has a vowel on one side, it has an even number on the other. Which cards must you turn over to test the rule?

Researchers have used versions of this puzzle since the 1960s, and only a small share of people get the abstract version right the first time. Take your guess before reading on.

The answer: A and 7

• A must be checked. It is a vowel, so an odd number behind it would break the rule.
• K can be ignored. The rule says nothing about consonants.
• 4 can be ignored, and this is the popular mistake. The rule says vowels need even numbers, not that even numbers need vowels.
• 7 must be checked. A vowel behind an odd number would break the rule.

Why we miss it

We tend to look for examples that confirm a rule instead of examples that could break it. Turning over the 4 feels useful, but no result on its back could prove the rule wrong.

A rule of the form if P then Q fails in exactly one way: P is true and Q is false. So check every card that might be P, and every card that might be not Q. Everything else is decoration.

Use it this week

Next time you want to test a belief, ask what would prove it wrong, and go look there first. It is less comfortable and far more informative.