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Logic Application: Guess Your Card

Necessary Background

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.


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 (1) page paper or more if needed in which you:

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

Solution Preview

Salient facts:
Andy sees Belle's, Carol's and my hand. The cards in Belle's hand total 16 and the cards in Carol's hand total 12.
Belle sees Andy's, Carol's and my hand. She says she sees a 1, 3, 5, 7, and 9. Andy's hand has 1, 5, and 7. Carol's hand has no odd ...

Solution Summary

This solution shows how to use logic to win a game of Guess Your Card. You and three other players hold 3 cards to your foreheads so that you can see each other's cards but not your own. Based on how the other players answer standard questions, you must determine what cards you hold.
The solution analyzes a sample game and reconstructs step by step the method that one player used to win.