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Puzzle | Four Card (A, D, 3, 6) | The Famous Four Card Task

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  • Difficulty Level : Easy
  • Last Updated : 18 Nov, 2021

Puzzle:
Suppose there are four cards labeled with the letters A, B, C, and D and the numerals 3, 4, 5, and 6. It is known that every card has a letter on one side and a number on the other. The rule of the game is that a card with a vowel on it always has an even number on the other side. How many and which cards should be turned over to prove this rule to be true?

Solution:

Step 1: There are four cards labeled as A, B, C, and D.

Step 2: One side of each card has a letter and another side has a number. It is known that a card with a vowel has always an even number on the other side. There is only one vowel card in the deck i.e. A. This means that the number on the other side of A can be 4 or 6. These are the only two even numbers. Let’s assume we have number 4 on the other side of card A.

Step 3: It is very intuitive that the rule ” A card with the vowel has an even number on the other side” can be proven to be true by turning two cards. 
Step 4: The first one will be the A(vowel) card to verify it does actually have an even number on the back and also the 3(odd number) card to verify that it does not have a vowel on the back.
Step 5: Turning only these two cards prove this rule to be true. We need not turn any more cards because the puzzle does not exclude the possibility of saying a consonant card having either an odd or an even number on the back.

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