Linda Rodriguez

Dr. George Maruschock

Math 104

January 27, 2013

The specific course learning for this paper is to solve problems using concepts from set theory and logic and use technology and information resources to research issues in algebra. The project given to the class uses the game of Guess Your Card. Each player draw three cards. Each card has a number between 1 and 9 on it. The players then place their cards on the heads so that everyone but the players can see the cards. The object of this game is to guess what cards you have in your hand without looking at your specific cards. The facts of the game are as follows: Andy has cards 1, 5 and 7; Belle has cards 5, 4 and 7; Carol has cards 2, 4 and 6. So part of the solution to this problem is that I will also need to determine what cards I have in my hand. The first player, Andy, draws the question card, “Do you see two or more players whose cards sum to the same value?”. He answers yes. Next Belle draws the question card, “Of the five odd numbers, how many different odd numbers do you see?” Belle’s answer is “All of them”. At this point, Andy speaks up, “I know what I have,” he says. “ I have a 1, a 5 and a 7 card.” The strategy I will be using to solve this problem is logic. I will also be using Polya’s Method in coming to the conclusion as to what cards I have in my hand and how Andy determined he had the 1, 5 and 7 card. I will be starting this game with a plan in place. I know what cards my opponents have and by listening to the answers given by each opponent to the questions they pose, I will be able to determine what cards I am holding in my hands. So once I start seeing a pattern in the game, I will be able to determine the answers to the question: what cards do I have in my hand? We must first look at the stated facts in the problem. We know that Andy has cards 1, 5 and 7; Belle has cards 5, 4, 7 and Carol has cards 2, 4 and 6. When Andy draws the question card, “Do you see two or more players whose cards sum to the same value?”, we must remember that he is also looking at the cards in my hands. So Andy determines that the sum of the cards in Belle’s hands is 16, the sum of Carol’s cards is 12, so subsequently the cards in my hands must total one of these two amounts. So in answering the question, Andy says “yes.“ But we must go a little further to determine what cards I hold in my hand. The next player, Belle, draws the question card which says, “Of the five odd numbers, how many different odd numbers do you see?” Her answer is “all of them”. The reason she answers all of them is because the odd numbers between 1 and 9 are obviously 1, 3, 5, 7 and 9. This means that since Andy is holding 3 of the five odd numbers, those being 1, 5 and 7 and