Answer to Riddle #80: Four Cards A, D, 3 & 6

80. Suppose I give you four cards labelled with the letters A and D and the numerals 3 and 6. The rule of the game is that a card with a vowel on it always has an even number on the other side.

Which of the cards would you have to turn over to prove this rule to be true?

Found this puzzle in Malcolm Gladwell excellent book the Tipping Point, he uses it to show how people instinctively get it wrong, we'll be getting it right:

some playing cards with letters and numbers on one side A, D, 3 & 6Before reading the answer can I interest you in a clue?

So you have to turn over two cards.

Both the 'A' card (to verify it does actually have an even number on the back) but also the '3' to verify that it does not have a vowel on the back.

It's perhaps easy to see how one of these is more obvious than the others. We don't need to turn over any of the others because the question does not exclude the possibility of say a non vowel card having either an odd or an even number on the back.

Further Thoughts

Of course the question also doesn't exclude the possibility of an non vowel card having a picture of a dog on the back.

We can't actually say that we have 'proven' the rule. Just that we have not violated it.





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