- 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?
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.
Analytical Solution
