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LESSON 4 · Think Like a Mathematician

The Four Card Puzzle

Four cards show A, K, 4, 7. Rule: "If a card shows a vowel on one side, it has an even number on the other." Which cards must you flip to test the rule?

Most people say A and 4. The correct answer is A and 7. Check A (does a vowel have an even number?) and 7 (does an odd number hide a vowel, which would break the rule?). Flipping 4 tells you nothing — the rule never says even numbers must have vowels.

This is the Wason selection task (1966), and fewer than 10% of people solve it correctly — including PhD students. Humans are terrible at testing "if P then Q" unless the content involves social rules.