This problem is a short, sharp lesson in what it means to check a rule. The winner is not whoever turns the most cards, but whoever rigorously distinguishes which ones could refute it.
The four cards
Riddle statement
Envelope the mesa there are four cards. Each one has a letter on one side and a number on the other.
You see these faces:
A D 4 7
You want to check if this rule is true:
“If a card has a vowel on one side, then it has an even number on the other.”
Which cards do you need to turn over, and only those?
Show solution
Solution
Answer: You have to turn A and 7.
Explanation:
The rule states that every vowel has an even number on the back. To check it, it is not enough to confirm favorable cases: you have to look for possible counterexamples, that is, a vowel with an odd number on the other side.
A must be turned: if an odd number appeared behind it, the rule would be refuted.
D is not necessary: the rule does not impose any conditions on the consonants.
4 is also not necessary: A card with an even number can have a vowel or a consonant behind it without violating anything.
7 it does have to be turned: if a vowel appeared behind it, we would have exactly the prohibited case—vowel with odd—and the rule would be false.
The only necessary cards are, therefore, A and 7.