The following project uses the game of Guess Your Card. This is a game in which each player draws (without looking) three (3) 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 the players 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 he /she sees (not the player's cards, which the player cannot see).

An Example

• Andy has the cards 6, 6, and 7
• Belle has the cards 3, 6, and 7
• Carol has the cards 1, 1, and 9
• Dan has the cards 3, 4, and 8

Andy draws the question card, "How many 7's 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 (2) more.

Situation

You are playing Guess Your Card with three (3) other players. Here is what you see:

• 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 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."

Write a one to three (1-3) page paper in which you:

1. Summarize the salient facts of the problem.
2. Explain your strategy for solving the problem.
3. Present a step-by-step solution of the problem.
4. Clearly state your answer.

Your assignment must follow these formatting requirements:

• Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions.
• Include a cover page containing the title of the assignment, the student's name, the professor's name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.
• 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 (8 1/2 × 11), and uncrumpled.
  • 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.

The specific course learning outcomes associated with this assignment are:

• Solve problems using concepts from set theory and logic.
• Use technology and information resources to research issues in algebra.
• Write clearly and concisely about algebra using proper writing mechanics.