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Four Cards (Posted on 2014-04-10) Difficulty: 3 of 5
  1. Five friends Alice, Ben, Carla, Dan, Ellen and Frank guess at four aces.
  2. Although nobody gets all answers right, there is a clear winner.
  3. Two people are tied for second-best score, and two others are tied for third-best score.
The guesses are as follows:
        1st Card      2nd Card    3rd Card    4th Card    
Alice     Spade       Spade       Club        Diamond     
Ben       Heart       Diamond     Diamond     Club        
Carla     Diamond     Club        Heart       Spade       
Dan       Diamond     Heart       Spade       Club        
Ellen     Heart       Spade       Club        Diamond 
Frank     Club        Spade       Diamond     Heart
What are the four cards?

No Solution Yet Submitted by K Sengupta    
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Solution Solution | Comment 1 of 2

There are six people.  From clues 2 and 3 we can deduce that one person had 3 correct guesses, two people had 2 correct guesses, two people had 1 correct guess, and one person had 0 correct guesses.

So there are a total of 9 correct guesses across the 4 cards.  That means at least one card got at least 3 correct guesses.  The only possibility is the 2nd card, which is spades.

That leaves 6 correct guesses across the other 3 cards.  If a card had only 1 or fewer correct guesses, then another of the cards would have to have 3 or more correct guesses, but there are none like this left.  Thus the remaining three cards each have two correct guesses, and so we know:

The 1st card is either heart or diamond.

The 3rd card is either club or diamond. 

The 4th card is either club or diamond.

From this we can see that the 1st card must be hearts. 

Finally, the 3rd card can't be clubs, because that would make the 4th card diamonds, and this would mean Ellen got all four correct. 

Thus we have

1 = heart
2 = spade
3 = diamond
4 = club

  Posted by tomarken on 2014-04-10 13:43:47
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