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.”
Andy suddenly speaks up. "I know what I have," he says. "I have a one, a three, and a