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Checking the Four Cards (illustration)
FILE No.78Unsolved

Checking the Four Cards

Difficulty ★★★about 6 minLogic PuzzleChecking a ruleContrapositive
Rule: vowel on one side means even number on the other. Cards: E, K, 4, 7. Which must be flipped?

Case Record

Four cards lie on a table. Each card has a letter on one side and a number on the other. The visible faces are:

E　K　4　7

A man claims: "If a card has a vowel (A, E, I, O, U) on one side, then it has an even number on the other."

You want to check whether his claim is really true, flipping only the cards you absolutely must.

Your question

Which cards should you flip?

Case Files

Evidence

Diagram

Does it need flipping?CardFlip?WhyEYesOdd on the back would break the ruleKNoA consonant is unrelated4NoNo back can break the rule7YesA vowel on the back would break it
Diagram

Timeline

  1. Four cards are laid out.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

What kind of card would break the claim?

Open hint 2

Can anything on the back of K or 4 break the claim?

Open hint 3

What if the back of the odd card is a vowel?

Solve It

Your question

Which cards should you flip?

Choose the answer closest to the truth.

Share: I'm solving this

The Truth

E and 7

The answer is: E and 7.

The claim is broken only if some card has a vowel on one side and an odd number on the other.

  • E (a vowel): its back must be even. You must check.
  • K (a consonant): the rule says nothing about consonants, so K cannot disprove it.
  • 4 (even): the rule does not say that even numbers must have a vowel on the back, so this card cannot disprove it.
  • 7 (odd): if its back is a vowel, the claim is broken. You must check.

So you only need to check the vowel card and the odd card.

Hunt for a counterexampleCounterexample = a card with a vowel and an odd numberOnly E and 7 could possibly be oneSo flip E and 7
Diagram of the solution

Key Points

  • Think about what a counterexample looks like
  • A counterexample is "vowel with an odd number"
  • Only check cards that could be counterexamples

Why people get fooled

People want to confirm cards that fit the rule (like the 4) instead of hunting for a counterexample.

Similar tricks

  • The counterexample-hunting type
  • The contrapositive type

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