Document Preview: Logic Application Project
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 ?rst 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.
NextBelledrawsthequestioncard,“Ofthefourevennumbers,howmanydi?erentevennumbers
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.
The Project’s 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 ?ve odd numbers, how many di?erent odd numbers
do you see? She answers “All of them.”
Andy suddenly speaks up. ”I know what I have,” he says. ”I have a one, a three, and a seven.”
The Question
What cards do you have?
In answering this question, you must write a neat and professional report. You need to brie?y
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...