I am playing a card game called Guess Your Card with three other players, Andy, Carol and Belle. The concept of this game is draw three cards out of a pile of cards where each card has a number between 1 and 9. You, along with the other players, must place these cards on your head without looking at them. Everyone but you should be able to see your cards. There is also another set of question cards that each player must draw from. Players can begin to predict which cards they possess by listening to other players answer questions from this deck. The player who draws a question card must answer the question on each card they draw. They answer these questions based on the other players cards, not their own. The object of the game is to guess what cards you have before anyone else does.
I can figure out what cards I have by listening to each question and answer and directly relating them to my own cards. Through the process of elimination, and simple math I can determine which cards I hold.
My cards are 4, 5, & 9. I determined the answer to this question by analyzing the following questions and answers. The first question drawn by the player, Andy, was, “Do you see two or more players whose cards sum to the same value?” The player answered “yes”. Looking at the other two players cards I determined:
Sum of Belle’s cards = 3 + 4 + 7 = 14
Sum of Carol’s cards= 4 + 6 + 8 = 18
Since these have different sums, but Andy sees at least two players whose cards have the same sum, then my cards must add up to either 14 or 18.
The next player, Belle, draws a question card, “Of the five odd numbers, how many different odd number do you see?” Belle answers, “All of them”. The only odd cards that Belle sees from Andy and Carol are 1, 3, & 7. So, this means I have a 5 and a 9.
I already know that the sum of my cards needed to be either 14 or 18. The sum of the cards I already