Card Hypothesis Puzzle

FACT: Each card has a number on one side and a letter on the other.
HYPOTHESIS: Every card that has a vowel on one side has an even number on its opposite side.

THE TEST: Which card or cards must you turn over in order to test the Hypothesis?

card-puzzle1

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The 15 possible answers are:

All four cards: A B C D
Three cards: A B C / A B D / A C D / B C D
Just two cards: A and B / A and C / A and D / B and C / B and D / C and D
Just one card: Card A only / Card B only / Card C only / Card D only

35 thoughts on “Card Hypothesis Puzzle”

  1. You must turn over every card. As the saying goes “leave no stone unturned”. In order to fully test the hypothesis we must look at all possible outcomes. It would seem that we could just turn over card A an card C, however that would only test that there is an even number on the other side of cardA and a vowel on the other side of cardC which leaves out the possibility that there is not a vowel on the other side of cardD or that there is an even number on the other side of card B.

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  2. You would turn over just Cards A and C. You would do so because the hypothesis only says “vowels and even numbers”. Therefore flipping cards B and D would not help you prove or disprove your thesis.

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  3. A and D because you need to prove card A has a even number on back, and also card D because you need to prove there is not a vowel on back.

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  4. Card a b and c because although a and c are a vowel and number, at least one other must be turned to make sure it is not a vowel or even number if the other side wasn’t, as that would disprove the theory

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  5. You would have to turn over every card to test this hypothesis because even if you only turn over cards A & C, that have one vowel and one even number, there’s a possibility cards B & D can have a vowel and an even number. Although card B has a consonant on one side, there is a possibility it could have an even number on the other side. Just like card D can have a vowel on the other side. You have to look at all of the possible outcomes, not just the two cards.

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  6. You will have to turn over every card. The idea is that you are actively trying to disprove your hypothesis. People who say that they only need to flip over A and C are simply looking for evidence to support their hypothesis, not actually challenge it. What if card D has a vowel? What if card B has an even number?
    You have to rigorously test all possible outcomes to remain true to the scientific method.

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    1. Correction: the statement is worded as “if p then q”, not “if and only if”. The english language is tricky like that. As such, the only cards that you have to flip are A and D.

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  7. You must turn over A, C, and D in order to prove the hypothesis. if card A has a even number then the hypothesis could still be true. If card C has a vowel on it then the hypothesis can still be true. If card D has a vowel on it then we know that not all cards with a vowel on it have an even number. Card B does not have a vowel on it so it does not relate to our hypothesis.

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  8. A B C D must be flipped over, as not only would the two cards that are involved in the hypothesis need to be proved to follow the hypothesis in order for it to be true, the other two cards would have to be proven to not follow the hypothesis, as one is a consonant and the other is an odd number.

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  9. In order to test the hypothesis you need to turn over cards A,C, and D. If all 3 match the hypothesis there is a 75% chance of card B matching as well.

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  10. Turning over all four cards would be the most direct way to confirm the hypothesis. If someone turns over just one card, two cards, or three cards, it doesn’t definitely prove the hypothesis. Just because some of the cards support the hypothesis it doesn’t mean they all do.

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  11. You would turn over A,C, and D. You could say turn over every card however, you are only trying to prove that each card with a vowel on one side has an even number on its opposite and card B is not a vowel.

    At first i said A and C

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  12. we should flip the cards A and C because ONLY they have a even number one of the side. so there are possibility of having a even number on the other side of the card A and also having a vowel on the other side of card C.

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