You are playing Guess Your Card with three other players. Here is what you see:
•Andy has the cards 1, 3, & 7
•Belle has the cards 3, 4, & 7
•Carol has the cards 4, 6, & 8
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 many different
odd numbers do you see?” She answers “All of them.”< /font>
Andy suddenly speaks up. "I know what I have," he says. "I have a one, a three, and a seven."
The Questions
1. What cards do you have?
In answering this question, you must write a neat and professional report. You need to briefly summarize the salient facts of the problem, explain your strategy for solving the problem, explain why your strategy will work, execute your strategy, show your mathematical working, draw conclusions from your working, and finally present your answer with a brief summery of why it is your conclusion.
2. Remember, your strategy is to use more than logic. What kind of logic will you use?
1. Report:
In this game of Guess Your Card, there are four players: Andy, Belle, Carol, and the player – let's call them Player X. The available information is as follows:
Andy has the cards 1, 3, and 7.
Belle has the cards 3, 4, and 7.
Carol has the cards 4, 6, and 8.
Andy confirmed that at least two players have cards that sum to the same value.
Belle stated that all five odd numbers are present.
To find out what cards Player X has, a logical approach will be used. The strategy involves considering the information given by Andy and Belle, as well as analyzing the possible combinations of cards that would satisfy both of their statements.
2. Use of Logic:
The logic used in this scenario is deductive reasoning. By carefully examining the given information, it is possible to deduce the set of cards held by Player X. This deductive approach allows us to form conclusions based on the available facts.
Now, let's execute the strategy and determine the cards held by Player X.
Since Andy mentioned that there are at least two players with cards summing to the same value, we can try to identify the possible combinations that meet this requirement. The only combination that fulfills this condition is having Andy and Belle holding the same sum of cards: 3 + 7 = 10.
Next, Belle stated that she sees all five odd numbers. Taking into account the sum of 10 formed by Andy and Belle's cards, Player X must hold the remaining odd numbers: 1, 5, and 9.
To summarize, my conclusion is that Player X has the cards 1, 5, and 9.
In conclusion, Player X's cards are 1, 5, and 9. This conclusion is reached by employing a deductive reasoning strategy, considering the information provided by Andy and Belle, analyzing the possible combinations, and drawing logical conclusions based on the given facts.