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Five Cards III (Posted on 2015-03-13) Difficulty: 3 of 5
  • Andy, Belinda, Carl, and Debbie guess at four aces and a joker.
  • Each card is correctly identified by at least one person.
  • Nobody gets them all right or all wrong.
  • No two people make the same number of correct guesses.
The guesses are as follows:
           1st Card    2nd Card   3rd Card    4th Card   5th Card
Andy        Club         Joker      Heart     Diamond     Club
Belinda    Diamond       Joker      Heart      Club      Spade
Carl        Heart        Club       Spade     Diamond    Joker  
Debbie     Diamond       Joker      Club       Club      Spade
What are the five cards?

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Analytical Solution | Comment 2 of 3 |
Well, if all scores are different and nobody get them all right or all wrong, then the total correct guesses by person must 1, 2 , 3 and 4, in some order.  Total correct guesses = 10.

Because of card 2, we cannot have 2 correct guesses per card.  So the correct guesses by card must be 3,2,2,2 and 1 in some order.  The 3 correct guesses are card 2 (Joker).

Consider card 5.  It is either a club or a spade.  If it is club, then cards 1, 3 and 4 were each guessed twice apiece, but this would mean that card 1 is a diamond and card 4 is impossible.  So card 5 cannot be the club.  It is the spade, which was correctly guessed twice.  

By the same logic, Card 3 cannot be a club.  So it is a heart, which was correctly guessed twice.

So which card was correctly guessed just once?  It cannot be card 4, so it is card 1, the club.

Making card 4 the diamond.

Cards (in order) are Club, Joker, Heart, Diamond, Spade.

Checking:
Andy correctly guessed 4, Belinda 3, Carl 1, and Debbie 2.

Pot's right.

  Posted by Steve Herman on 2015-03-14 10:46:30
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