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Guess That Card

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Guess Your Card
Steven Colson
Prof. Latriece Tanksley
MAT-104
August 6, 2013

The name of this guessing game is Guess Your Card. The purpose of this project is to employ various logical methods to figure out which cards each player possesses. The game is completed and won by the first player to correctly state what card he or she has. In this particular game setup there are 4 players, Andy, Belle, Carol and Myself. Each player picks 3 cards without looking at them, cards ranging from 1 thru 9. Andy has the cards 1, 5, and 7. Belle has the cards 5, 4, and 7. Carol has the cards 2, 4, and 6. As of right know I do not know what numbers I have in my possession. Andy draws the question card, “Do you see two (2) or more players whose cards sum to the same value?” He answers, “Yes.” Next Belle draws the question card, “Of the five (5) odd numbers, how many 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, a 5, and a 7." To figure out what numbers I have in my possession, I will use the process of elimination. I know the numbers of the other players, and information given by the other players I can solve the answer of what are my card numbers. To first solve this problem, I remember that Andy said that he saw two (2) or more players whose cards sum to the same value. So knowing this I know that 2 of the players’ numbers will add up to the same sum. So I add both Belle and Carol card numbers individually and find out that their sums are different. The information gained from this tells me that my numbers, if added together will be the same as either Belle or Carol’s Cards. Next, I will take in consideration the information given to me by Belle. Belle draws the question card, “Of the five (5) odd numbers, how many different odd numbers do you see?” She answers, “All of them.” So with this new information gained I now know that all the odd numbers are visible to Belle, meaning the numbers 1, 3, 5,7and 9. Using the process of elimination I derive, that numbers 3 and 9 are not held by the other players, so they must belong to me. I now know that 3 and 9 are two of my numbers and I only need to find out my third number. My two numbers were 3 and 9 for a sum of 12, so the sum of those two numbers and my third number will be the same as either, Belle and Carol. Carol’s card added up to a sum of 12, but two of my cards added up to that sum so I can eliminate Carol as having the same sum. The only choice left is 4, which if added up gives me the sum of 16 and is identical to the sum that Belle possesses. My numbers are 3, 4, and 9.

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