- Five friends Alice, Ben, Carla, Dan, Ellen and Frank guess at four aces.
- Although nobody gets all answers right, there is a clear winner.
- Two people are tied for second-best score, and two others are tied for third-best score.
The guesses are as follows:
1st Card 2nd Card 3rd Card 4th Card
Alice Spade Spade Club Diamond
Ben Heart Diamond Diamond Club
Carla Diamond Club Heart Spade
Dan Diamond Heart Spade Club
Ellen Heart Spade Club Diamond
Frank Club Spade Diamond Heart
What are the four cards?
There are six people. From clues 2 and 3 we can deduce that one person had 3 correct guesses, two people had 2 correct guesses, two people had 1 correct guess, and one person had 0 correct guesses.
So there are a total of 9 correct guesses across the 4 cards. That means at least one card got at least 3 correct guesses. The only possibility is the 2nd card, which is spades.
That leaves 6 correct guesses across the other 3 cards. If a card had only 1 or fewer correct guesses, then another of the cards would have to have 3 or more correct guesses, but there are none like this left. Thus the remaining three cards each have two correct guesses, and so we know:
The 1st card is either heart or diamond.
The 3rd card is either club or diamond.
The 4th card is either club or diamond.
From this we can see that the 1st card must be hearts.
Finally, the 3rd card can't be clubs, because that would make the 4th card diamonds, and this would mean Ellen got all four correct.
Thus we have
1 = heart
2 = spade
3 = diamond
4 = club
Posted by tomarken
on 2014-04-10 13:43:47