- Andy, Brenda, Carl, Della, and Enoch guess at four aces and a joker.
- Each card is correctly identified by at least one person.
- 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?
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