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Five cards (Posted on 2014-02-04) Difficulty: 3 of 5
  1. Andy, Brenda, Carl, Della, and Enoch guess at four aces and a joker.
  2. Each card is correctly identified by at least one person.
  3. All five people make the same number of correct guesses.
The guesses are as follows:
        1st Card    2nd Card    3rd Card    4th Card    5th Card
Andy     Spade       Heart        Club       Joker      Diamond
Brenda   Spade       Joker       Diamond     Club        Spade
Carl     Club       Diamond       Spade      Joker       Heart
Della   Diamond      Heart        Joker      Club        Spade
Enoch    Club        Joker       Diamond     Spade       Heart
What are the five cards?

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Counting Cards (spoiler) Comment 1 of 1

Well, let's start by counting the maximum number of total correct guesses. No card has three guesses the same, so the number of correct guesses for any given card is at most 2, so the maximum correct guesses for all 5 cards is at most 10. Therefore, the number of correct guesses per person is 1 or 2.

And it can't be 1 correct guess per person, because that would require each card to be guessed exactly once. But an examination of the guesses shows that whichever card Brenda guessed correctly, somebody else necessarily guessed the same card correctly.

So, we can conclude that each person made 2 correct guesses. And since no card has three guesses the same, it follows that each card was correctly guessed exactly twice.

This means that Card 3 is a diamond (score one for B and E).

Card 1 is either a Spade (guessed by A and B) or a Club (guessed by C and E).
Card 4 is either a Club (guessed by B and D) or a Joker (guessed by A and C).
Card 2 is either a Joker (guessed by B and E) or a Heart (guessed by A and D).
Card 5 is either a Heart (guessed by C and E) or a Spade (guessed by B and D).

If Card 1 is a spade, then card 4 must be the Club, then card 2 must be the Joker, then card 5 must be the Heart. But this leaves B with 4 correct guesses. So card 1 is not the Spade.

The Cards must therefore be as follows:
Card 1 Club (guessed by C and E)
Card 4 Joker (guessed by A and C)
Card 2 Heart (guessed by A and D)
Card 5 Spade (guessed by B and D)
Card 3 Diamond (guessed by B and E)

Edited on February 4, 2014, 9:51 pm
  Posted by Steve Herman on 2014-02-04 19:36:12

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