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Guess Your Card

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Algebra with Applications 104 | Assignment 1: Logic Application- Guess Your Card | | 10/31/2013 |

Guess Your Card is when each player draws three cards without looking. Each card has a number between 1 and 9 on it. The players then place their cards on their heads so that everyone but that person can see their own cards; the purpose is so that you can guess which card you have |

I am playing Guess Your Card with three (3) other players. Andy has the cards 1, 5, and 7; Belle has the cards 5, 4, and 7; Carol has the cards 2, 4, and 6. Andy draws answers yes to the question card, “Do you see two (2) or more players whose cards sum to the same value?” 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." Andy draws the question card, “Do you see two or more players whose cards sum to the same value?” He answers, “`yes.”
The sum of Belle's cards 5+4+7 = 16 sum of Carol's cards = 2+4+6 = 12 I found that there are 2 different sums but Andy sees at least two players whose cards have the same sum, which means my cards either adds up to 12 or 16 . If the only odd cards Belle sees are 1, 5, 7 from Andy then I must have a 3 and a 9 which equals 12. My sum either is 12 or 16 and since 3 + 9 = 12, and smallest card is 1, then my cards must add up to 16. We know now that my cards must equal 16 and that I have two cards both 9 and 3 which add to 12. 16-12=4 my cards are 9, 3, and 4. Going over my work
Step 1 If Andy sees 5, 4, 7 from Belle and 2, 4, 6, from Carol the sum are 16 and 12
Step 2 Belle sees 5 odd cards 1,5,7 are of Andy
Step 3 The game has cards 1-9 Belle sees 5 odd card 1, 5, and 7 leaving 3 and 9 to be my cards
Step 4 We know that my cards equals 16 so 16-9-3=4
Answer: I have cards 3, 4, and 9

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