FACT: Each card has a number on one side and a letter on the other.
THESIS: Every card that has a vowel on one side has an even number on its opposite side.
REBUTTAL: Which card or cards must you turn over in order to test whether or not the Thesis is true?
Write your answer on an index card.
WHY WE CAN’T TURN ALL THE CARDS OVER.
Turning over all the cards is of course a reasonable plan, but it’s forbidden by the challenge of the puzzle, which asks “Which card or cards MUST you turn over?”
WHY WE MUST TURN OVER CARD A
The Thesis states specifically that “every card that has a vowel on one side has an even number on its opposite side.” To test that thesis, we MUST turn over card A. Anything other than an even number would refute the thesis.
WHY WE CAN IGNORE CARD B
The Thesis says nothing about consonants. Nothing on the other side of card B could prove or refute the thesis.
WHY WE CAN IGNORE CARD C
The Thesis says nothing about what’s on the other side of an even-numbered card. Yes, a vowel on one side requires an even number on the other; but an even number places no obligation on the other side. Does an even number together with a consonant refute the Thesis? No.
WHY WE MUST TURN OVER CARD D
A vowel on the other side of card D would refute the Thesis.
WHAT CARD OR CARDS MUST YOU TURN OVER?
A and D.
Only 4% of test subjects answer correctly.
WHY WE’RE FOOLED BY THE PUZZLE
—First, we’re desperate for symmetry. When someone tells us all vowel cards are even, we automatically conclude that all even cards are vowels. We’re wrong, but it happens.
—Second, we mistakenly believe that supportive examples prove a Thesis, but they don’t, at least not a Thesis that makes a categorical claim such as “Every card.” No number of supportive cards can prove such a Thesis, but a single exception can refute it.
—”Every clover has three leaves” is not proved by millions of three-leaf clovers, but it is refuted by a single four-leaf clover.
—On the other hand, the fix is easy: “Every clover has at least three leaves.”
Rowan Counterintuitive 