1 page/≈275 words
Mathematics & Economics
Logic Application (Essay Sample)
Necessary Background The following project uses the game of Guess Your Card. This is a game in which each player draws (without looking) three cards. Each card has a number between 1 and 9 on it. The players then place their cards on their heads so that everyone but themselves can see the cards. The object of the game is to guess what cards you have. The first person to do this correctly wins. During the play, each player, in turn, draws a question at random from a stack of questions. The player then answers the question based on the cards that they see (not their own cards, which they cannot see). An Example Andy has the cards 6, 6, & 7 Belle has the cards 3, 6, & 7 Carol has the cards 1, 1, & 9 Dan has the cards 3, 4, & 8 Andy draws the question card, “How many 7s do you see?” He answers, “one,” because he cannot see the 7 on his own head; he sees only the 7 on Belle's head. Next Belle draws the question card, “ Of the four even numbers, how many different even numbers do you see?” She answers, “Three,” because she sees the 4, 6, and 8 on Andy and Dan's head. From this, Dan can conclude he has two even cards, since he can only see a 6 and Belle sees two more. Situation You are playing Guess Your Card with three other players. Here is what you see: Andy has the cards 1, 3, & 7 Belle has the cards 3, 4, & 7 Carol has the cards 4, 6, & 8 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?” She answers “All of them.”< /font> Andy suddenly speaks up. "I know what I have," he says. "I have a one, a three, and a seven." The Questions 1. What cards do you have? In answering this question, you must write a neat and professional report. You need to briefly summarize the salient facts of the problem, explain your strategy for solving the problem, explain why your strategy will work, execute your strategy, show your mathematical working, draw conclusions from your working, and finally present your answer with a brief summery of why it is your conclusion. 2. Remember, your strategy is to use more than logic. What kind of logic will you use? The format of the report is to be as follows: Typed, 1 to 3 page report, double spaced, Times New Roman font (size 12), one inch margins on all sides, APA format. In addition to the 1 to 3 pages required, a title page is to be included. The title page is to contain the title of the assignment, your name, the instructor's name, the course title, and the date. Include the Grading Procedure page in your report. Neatness and professionalism of presentation: Text should be legible on white paper with black ink. Pages should be stapled, without frilly edges, of regular size (81/2 × 11), and un-crumpled. Use sentences and paragraphs appropriately. Text should be free of typos and spelling mistakes. Presentation should include an opening statement describing what you intend to present and a conclusion wrapping up the presentation. source..
Considering the situation at hand, it will be easy using logic to determine the cards one has because one can see the cards on the other friends’ heads. With the two questions raised by the other friends, one will need to consider the answers given to determine what one has. For example, if an answer is given that a friend can see the three even numbers in total and the person in question can only see two even numbers, it is evident that he must have the third even number. This will be through pure logic, without any mathematical calculations.
In this case, it is very easy to determine the cards I have because the two questions raised and the answers given are sufficient to determine the cards I have on my head. Andy raises...
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