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?
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.
Thinking outside the deck (spoiler)
