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Words 398

Pages 2

Shannon Will

Professor Taylor

Algebra with Applications

May 31, 2012 I am playing “Guess Your Cards” with Andy, Belle, and Carol. Andy has drawn a 1, 3 & 7, Belle a 3, 4 & 7, and Carol a 4, 6 & 8. No one can see their own cards. Question cards are drawn and asked to help each player deduce what their own cards are. I believe deductive reasoning would be the logic used to solve this problem; you have the facts in front of you. The deck has only cards with the numbers 1 through 9 on them, you can see the cards already drawn and deduct, by the answers to the questions, exactly what cards you have. Let’s start with the first question. “Do you see two or more players whose cards sum to the same value?” Andy answers “yes”. Of the cards I can see, no two people have the same sum. I deduce that I must have the second set. Adding the cards of each person, I can see that Andy’s cards equal 11, Belle’s equal 14, and Carol’s equal 18. My set of cards must equal one of these. Second, “Of the five odd numbers, how many different odd numbers do you see?” Belle answers that she sees all of them. I can only see 1, 3, & 7. Therefore, I must have a 5 and a 9. These are the only two odd numbers that I cannot see. The statement that states that Andy knows what cards he has is totally irrelevant to the problem. It has absolutely no bearing on my logic or what cards I have. Knowing I have a 5 and a 9, I only have to figure out what my last card is. My 5 and 9 add up to 14, therefore, my sum cannot to be equal to Andy or Belle because Andy has 11 and I am already over that with only two cards, Belle has 14 and I am equal to that will only two cards. I have to equal 18 so my last card must be a 4. “5+9+4 = 18” I came to this my conclusion with pure and simple logic and nothing else. The only other way to figure your cards might be to...

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...Assignment 1: Logic Application Andy, Belle, Carol, and I are playing the game Guess Your Card. In the game, each person draws three cards without looking from a stack of cards containing contain multiple cards ranging in denomination from one to nine. Each person then places the cards on his or her forehead so that all of the other players can see the others’ cards, but cannot see their own. There is also a stack of questions that each person draws from in turn. These questions help the players deduct the identities of their own cards. We have shuffled the deck and each player has drawn three cards and placed them on their own forehead. Andy has drawn 1, 5, and 7; Belle has drawn 5, 4, and 7; and Carol has drawn 2, 4, and 6. Obviously I cannot see my own cards. Andy draws the first question, which asks, “Do you see two or more players whose cards sum to the same value?” To which he answers, “Yes.” Belle’s turn is next. Her card asks, “Of the five odd numbers, how many different ones do you see?” She responds, “All of them.” With these two questions, I am able to deduce which cards I have. After Andy drew the first question, “Do you see two or more players whose cards sum to the same value?” I added up Belle’s and Carol’s cards to see if theirs sum to the same total. Belle’s cards (5,4,7) add up to 16. Carol’s cards (2,4,6) add up to 12. Since Belle’s and Carol’s cards do not add up to the same amount, I can conclude that my cards add up to either 16 or 12. The next......

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...my head they are 1,5,and 7” Andy drew the question “Do you see two or more players whose cards sum to the same value?” to which he answered “Yes” . Andy’s cards sum to 13, Belle cards sum to 16 and Carol’s cards sum is 12. Therefore my cards must equal the sum of one of those numbers. My cards cannot sum to 12 like Carol’s because I need to have a third card on my head, so therefore my cards must equal 13 or 16. My cards cannot equal the sum of 13 because Andy said that he has a 1, 5, and a 7 on his head because he does not see a 1 on anyone else’s head. Therefore the remaining cards on my head must be a 4 to sum to 16 the same as Belle’s. The cards that I have are 3, 4, and9 which is the equal the sum of 16. You just have to use logic when handing out the playing card’s realizing that you are working with number 1 to 9 you have even and odd numbers that you are playing...

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