You are playing Guess you card with (3) other players. Here is wha you see:
Andy has the cars 1,5, and 7
Belle has the cards 5,4, and 7
Carol has the cards 2,4, and 6
Andy draws the question card, " do you see two or more players whose cards sum to the same value? He answers "yes"
next belle draws the question card, of the five odd numbers, how may different odd numbers do you see? She answers, "all of them"
Andy suddenly speaks up, "I know what I have," he says I have a 1, 5,and 7,
write a one page paper in which you:
1. Summarize the salient facts of the problem.
2. Explain your strategy for solving the problem.
3. Present a step by step solution of the problem
4. Clearly state your answer
1. Salient facts of the problem:
- Andy has the cards 1, 5, and 7.
- Belle has the cards 5, 4, and 7.
- Carol has the cards 2, 4, and 6.
- Andy confirmed that there are two or more players whose cards sum to the same value.
- Belle confirmed that she sees all five odd numbers.
- Andy suddenly declares that he knows his cards.
2. Strategy for solving the problem:
To solve this problem of Guess You Card, we need to analyze the clues provided by the players and deduce the cards they have. By considering the given information, we can narrow down the possibilities and determine everyone's cards.
3. Step by step solution:
a. Analyze Andy's response: Andy states that there are two or more players whose cards sum to the same value. From the given card sets, we can observe that the sum of Belle's cards (5 + 4 + 7 = 16) is the same as the sum of Carol's cards (2 + 4 + 6 = 12). Hence, Andy's confirmation aligns with this observation.
b. Analyze Belle's response: Belle claims that she sees all five odd numbers. Based on this statement, we can deduce that Andy does not have any odd-numbered cards (1 and 7) because Belle sees all odd numbers, but she doesn't mention them. Thus, Andy must have the card 5.
c. Deduce Carol's cards: With Andy having the card 5, we need to determine Carol's cards. Since we know that Belle has the cards 5, 4, and 7, and Andy has the card 5, Carol cannot have the card 5. Additionally, Carol's cards cannot be the same as Belle's, so she cannot have the cards 4 and 7. Therefore, Carol must have the cards 2 and 6.
d. Confirming Andy's declaration: Andy confidently states that he knows his cards, but he only revealed the card 5. Since we have determined that Andy's other cards cannot be odd numbers (1 and 7), we can conclude that his remaining card is the number 1.
4. Answer:
After analyzing the salient facts and deducing each player's cards, we can conclude that:
- Andy has the cards 1, 5, and 7.
- Belle has the cards 5, 4, and 7.
- Carol has the cards 2, 4, and 6.
Therefore, the answer is Andy has the cards 1, 5, and 7.