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?

4, 5, and 9. This way, you have all five odd numbers and 4+5+9=18 and 4+6+8=18 are of equal sums. Is this what you were looking for?

I need help on figuring why this is the answer. 4,5,9. i see how it all adds up.. but i am stuck on the over all reasoning

1. Summary of the problem:

We are playing a card game called Guess Your Card with four players - Andy, Belle, Carol, and the player (you) whose perspective this question is from. Each player has a set of three cards, and they take turns drawing question cards and answering them truthfully. Andy has the cards 1, 3, and 7, Belle has the cards 3, 4, and 7, and Carol has the cards 4, 6, and 8. Andy answers "Yes" to the question of whether he sees two or more players whose cards sum to the same value. Belle, later on, answers "All of them" when asked about the number of different odd numbers she sees.

2. Strategy for solving the problem:

To determine the cards you have, we can use deductive reasoning by considering the information provided by Andy and Belle and applying logical thinking to narrow down the possibilities.

3. Logical reasoning behind the strategy:

From Andy's response, "Yes," to the question about whether he sees two or more players whose cards sum to the same value, we can infer that the sum of his cards, i.e., 1 + 3 + 7, must be equal to the sum of another player's cards. This indicates that the player with the remaining set of cards (you) should have a sum that does not match any of the sums mentioned so far.

Additionally, Belle's response, "All of them," to the question about the number of different odd numbers she sees, implies that she can see all the odd numbers in the game. Since she does not have a 5, it means the player with the remaining set of cards (you) should have a 5.

4. Executing the strategy and mathematical working:

Given that Andy's sum is 1 + 3 + 7 = 11, and Belle can see all odd numbers except 5, we can deduce the following:

- Andy's sum (11) cannot be matched by Carol's cards (4 + 6 + 8 = 18), so you cannot have the same sum as Carol.
- Andy's sum (11) can be matched by Belle's cards (3 + 4 + 7 = 14), so you cannot have the same sum as Belle.
- Since Belle sees all odd numbers except 5, the sum of your cards must include the odd numbers 1, 3, 7, and 9 (to meet the requirement of having all odd numbers).

From the above deductions, the remaining possibility is that your cards consist of the numbers 1, 3, 5, 7, and 9.

5. Conclusion:

Based on the deductions, the cards you have are 1, 3, 5, 7, and 9.

In summary, by analyzing the given information and using logical reasoning, we concluded that the player's cards consist of the numbers 1, 3, 5, 7, and 9. This solution was derived by considering Andy's response regarding the sums of the cards and Belle's response about the odd numbers in the game.

6. Explanation of the type of logic used:

In this strategy, deductive reasoning and logical thinking were employed to narrow down the possibilities and arrive at a conclusion. By analyzing the provided information and applying the principles of logic, we could eliminate certain possibilities and deduce the composition of the player's cards. This type of logic is commonly used in problem-solving to make inferences and reach logical conclusions based on given information.