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# Assignment Logic

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Summarize the salient facts of the problem. Explain your strategy for solving the problem. Present a step-by-step solution of the problem. Clearly state your answer. Answer: The salient facts of this problem are that we are playing with a deck of cards 1-9. Andy is holding 1, 5 and 7. Carol is holding 2, 4 and 6. Belle is holding 5, 4 and 7. During Ands turn, he answers his question by saying that two or more of the three player’s cards that he can see has equal sums.

Belle then begins her turn by answering her question saying that out of the 5 odd numbers, she can see all of them.

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At the beginning of the game, I did not realize we were playing with a deck of cards with multiples of each number. Instantly, I used deductive reasoning to claim that I had 3, 8 and 9 since those were the only three numbers that were not being held up. But that was too simple, so instead of shouting it out that I figured it out, I waited to start the game.

Andy draws his question from the random deck and he answers it by saying that the sum of two or more players cards are equal to each other. Since Andy cannot see his cards, my attention is drawn to Belle’s and Carol’s. Belle is holding a 5, 4 and 7 giving her the sum of 16.

Carol is holding 2, 4 and 6 giving her the sum of 12. The sums of their cards do not match, so know that my cards will equal either 12 or 16. Now it is Belle’s turn. She draws her question card from the random deck and states that out of the 5 odd numbers in the deck, she sees all of them. Since Belle cannot see her cards, I focus on Ands and Carol’s. Andy is holding a 1, 5 and 7. However, Carol is not holding any odd numbered cards and Belle is unable to see her own. Once again using deductive reasoning, I have formed the conclusion hat two out of my three cards are a 3 and 9.

Now going back to Ands answer to his question, I know that two or more player’s cards have the same sum. So far I know that 3+9=12, therefore the sum of my three cards cannot equal 12. With deductive reasoning can conclude that the sum of my cards will equal 16. Therefore, if I subtract 12 from 16, I will find the value of my 3rd card. 16-12=4. That’s it! I know what I have: have 3, 9 and 4. This is my conclusion because the sum of my cards and the sum of Belle’s cards are equal while also fulfilling that all odd numbers can be seen on the board.

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