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Logic Applications

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I am playing a Guess your card game with 3 other people. Andy, Belle, Carol, and myself all draw three cards without looking. Each card has a number from 1-9 on it. We each drew 3 cards: Andy got cards 1, 5, and 7. Belle has the cards 5, 4, and 7, and Carol has the cards 2, 4, and 6. I’ll be using logic and the process of elimination to figure out what cards that I have. Also to see how Andy figured out his cards. Andy draws the question card, “Do you see two or more players whose cards sum to the same value?” He answers “Yes.”
Sum of Belle's cards = 5 + 4 + 7 = 16
Sum of Carol's cards = 4 + 6 + 2 = 12
The sum of Belle’s cards is 16 and Carol’s sum is 12. Thats means the sum of my cards must be 16, or 12. Next Belle draws the question card, “Of the five odd numbers, how many different odd numbers do you see?” She answers, “All of them.” If Belle sees all five odd numbers she sees 1,3,5,7, and 9. I can only see 3 different odd numbers so I must have the other 2 odd numbers that Belle can see. The remaining odd numbers that I must have are 3 and 9. Since the sum of 9 and 3 is 12 that is already the sum of what Carol has.The smallest 3rd number can only be 1. So I must have a sum of 16. My 3rd number must be a 4. The total sum of my cards is now 16, same as Belles. Now you see why Andy knew what cards he had. He realized that the only odd numbers Belle could see from Carol and I were 3 and 9, and yet she claimed she could see all five odd numbers. So the remaining three: 1, 5, 7 must have come from Andy himself. That's how he figured out what he had.

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