Cards!

Logic Level 3

Say we have a deck of 14 cards. They have a letter on one side, and a number on the other. Face up, they are: 1 , 2 , 3 , 4 , 5 , 6 , 7 , A , B , C , D , E , F , G . 1,2,3,4,5,6,7,A,B,C,D,E,F,G. Let's propose that on the back of any vowel card, there must be a prime. Find the minimum number of cards that must be flipped over to guarantee the validity of this statement.

5 4 2 7

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David Lee by David Lee , 20, USA

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3 solutions

Patrick Corn
Jul 21, 2014

You need to flip the vowels and the non-primes. There are 5 \fbox{5} of these.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ivan Koswara
Jul 21, 2014

A card showing a vowel has the potential to counter the claim (if the number behind it isn't prime). Similarly, a card showing a non-prime has the potential to counter the claim (if the letter behind it is a vowel). There are two vowels and three non-primes shown, so we need to turn over all these 2 + 3 = 5 2+3 = \boxed{5} cards.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sajjan Barnwal
Jul 22, 2014

total favourable outcomes =12 and total outcomes =49...........its more than 4 ....i.e. 5

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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