The Guess Your Card Game

In the Guess Your Card game each player draws three cards without looking at them. Each card has a number on it between one and nine. Then all of us place our cards on our heads so that we can only see our opponent’s cards but not the three cards we pulled. Our objective is to guess what cards we have ourselves. The first person to do this wins the game. Throughout game play, each player draws a question at random from a stack of questions. Then each player answers their particular questions based on the cards that they see from their opponents.
As previously stated each card has a number on it between one and nine. Andy’s cards are one, five and seven. Belle’s cards are five, four and seven. Carol has two, four, and six. We are solving for my cards which can be any number between one and nine.
The strategies used for solving the problem are inductive reasoning and deductive reasoning (process of elimination.) As questions are answered we are able to remove numbers from the one through nine answer set.
When Andy pulls the question card, “Do you see two (2) or more players whose cards sum to the same value? We can ignore his three cards (1, 5, and 7) because we know he could not see them, thus his sum of thirteen would not be one of the sums with the same value. Being able to see Belle’s cards (5, 4, and 7= 16) and Carol’s cards (2, 4, 6 = 12), I was able to conclude that my cars should equal twelve or sixteen. This is inductive reasoning. (a + b + c = 12 or 16)
Once Belle pulls the question card, “Of the five (5) odd numbers, how many different odd numbers do you see?” She answers, “All of them.” I was able to see Andy, Belle and Carol cards by using deductive and inductive reasoning along with the process of elimination I realized my first two cards were a three and a nine. I used a system equation to solve for my third and final card.
After all questions were answered and before Andy shouted out his card numbers I was able to eliminate 1, 2, 5, 6, 7, and 8, giving me my numbers of 3, 4, and 9. I was also able to conclude a + b + c = 16 by plugging in my numbers (3+9) [known from Belle’s answer] +c = 12 or 16. Since 1 ≤ c ≤ 9, c = 4 because c ≠ 0.
I cannot wait to play this game with friends and tell them how the game ties into my Algebra with Application course. | Andy | Belle | Carol | Tawana | C1 | 1 (x) | 5 | 2 | a=1, 2, 3, 4, 5, 6, 7, 8, 9 | C2 | 5 (y) | 4 | 4 | b==1, 2, 3, 4, 5, 6, 7, 8, 9 | C3 | 7 (z) | 7 | 6 | c==1, 2, 3, 4, 5, 6, 7, 8, 9 | Sum | 13 | 16 | 12 | a + b + c = 12 ora + b + c = 16 |