Logic Application
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.”
I attend to present on the solution of a set theory and logic problem using a deduction method. Based on the information provided, I will guess the cards I have on my head and explain the deduction methods. The salient facts of the problem are that Andy answers yes to the question, “Do you see two or more players whose cards sum to the same value.” Then Belle answers yes to the question, “Of the five odd numbers, how many different odd numbers do you see?” this means that Belle sees 1, 3, 5, 7, and 9. I also know that Andy has a 1, a 5, and a 7. Below are the three sets held by Andy, Belle, and Carol as follows: A = {1, 5, 7} B = {4, 5, 7} C = {2, 4, 6} My strategy for solving the problem is to use deductive reasoning and the process of elimination. I will then find the sum of each the sets. So we know that A = {1, 5, 7} and the sum is 13. B = {4, 5, 7} is 4 + 5+ 7= 16. C = {2, 4, 6} = 2 + 4+ 6 =12.
With the information given above I know that my cards must be equal to the sum of one of the above sets. Since the sums of Belle’s and Carol’s cards are not equal, then the sum of my cards must be equal to one of the players. Since I know that I have 3 and 9 and, it is not possible for my cards to be equal to the sum of Carol’s cards that has a total of 12, because I have three cards, and I know that U ={1,2,3,4,5,6,7,} That leaves me with 3 +9 + ? = ?. So then in order for my cards to sum to the same value as another player, then I must have a total of 16, Since 3 + 9 = 12 + 4 = 16, My cards are 3, 4, and 9. My set of cards is {3,4,9}, which means that the sum of my set of cards is equal to the sum of Belle’s set.