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Five Cards II (Posted on 2014-06-16) Difficulty: 3 of 5
Aaron, Belinda, Carlos, Debbie, and Ethan guess at four aces and a Joker. Each card is correctly identified by at least one person. At the conclusion, four persons are tied in the number of correct guesses, with the fifth person having just one correct guess fewer.
     
           1st Card   2nd card  3rd card  4th card  5th Card
Aaron      Club       Joker     Diamond   Club      Heart
Belinda    Joker      Spade     Club      Spade     Joker      
Carlos     Club       Club      Heart     Diamond   Joker
Debbie     Heart      Diamond   Diamond   Joker     Club
Ethan      Spade      Heart     Joker     Spade     Diamond
What are the five cards?

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Thinking outside the deck (spoiler) Comment 1 of 1
a) 4 people are tied with more than one correct guess, and the 5th has one.  So there must be at least 9 correct guesses.

b) Cards 1,3, 4 and 5 can be guessed correctly by at most 2 people.  Card 2 can be guessed correctly by at most one.  In total, there can be at most 9 correct guesses.

c) Therefore, there are exactly 9 correct guesses.  Any card that could be correctly guessed twice, was correctly guessed twice.

This makes:  
Card 1: Ace of Clubs
Card 3: Ace of Diamonds
Card 4: Ace of Spades
Card 5: Joker
Card 2: By process of elimination, if they all came from the same deck, then card 2 is the Ace of Hearts.

But maybe the cards came from different decks, and one ace is duplicated twice.  Let's check:

Aaron guessed card 1 and 3 correctly, so card 2 is not a joker.
Belinda guessed card 4 and 5 correctly, so the card 2 is not a spade.
Carlos guessed card 1 and 5 correctly, so card 2 is not a club.
Debbie guessed card 3 correctly, so card two might be a diamond.
Ethan guessed card 4 correctly, so card 2 might be a heart.

Expected answer:
Cards 1-5 are club, heart, diamond, spade, joker.  Debbie had just one correct guess.

Unexpected answer:
Cards 1-5 are club, diamond, diamond, spade, joker.  They do not all come from the same deck.  Ethan had just one correct guess.

  Posted by Steve Herman on 2014-06-16 16:08:29
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