Logic Application Project

Student Name: _______________________, _______________________ Last Name First Name

The Problem: How can you found out what cards you have?

The Approach: First, we should examine the stated facts that Andy has the cards 1 3 7 while Belle has the cards 3 4 7 and Carol has the cards 4 6 8. Then the second thing we will look at is their answer on the question cards that they draw. Combining the information given and their answers on the question cards, we can figure out what is the connection of these to your own cards, and that’s how we will figure out what cards you have.

Conclusion: First, by examining the stated facts that Andy has the cards 1 3 7 while Belle has the cards 3 4 7 and Carol has the cards 4 6 8, and the answer of Belle to his question card, knowing that she sees Andy, Carol and yours, she says that she sees all of them, the five odd numbers on the cards that she can see and Carol don’t have any odd number on her cards so the ones that are left is you and Andy. Andy has three odd numbers of each kind on his cards and that would leave a conclusion that you have two odd numbers on your cards.

Looking back to the answer of Andy to the question “Do you see two or more players whose card sum to the same value?” and answered “Yes”, knowing that the cards he can see are yours, Belle and Carol, and the sum of Belle’s cards and Carol’s cards are not the same, we can conclude that one of them have the same value or sum of the cards as of you. Then after knowing who have the same sum of cards as of you, you need to subtract the sum of your two odd number cards to the sum of the player that you conclude to be the same as yours. That would result to the last unknown card, by then you would know what cards have.

Solution Details:

Given:

1. Andy has the cards 1 3 7 2. Belle has the cards 3 4 7 3. Carol has the cards 4 6 8 4. two or more players have the same value of cards, excluding Andy 5. all the five odd numbers from 1 to 9 can be seen on the cards of other players excluding Belle

Find:

1. What cards do you have?

2. What kind of logic will you use?

Solution:

Answer to Question 1:

Given:

1. Andy has the cards 1 3 7 2. Belle has the cards 3 4 7 3. Carol has the cards 4 6 8 4. two or more players have the same value of cards, excluding Andy 5. all the five odd numbers from 1 to 9 can be seen on the cards of other players excluding Belle

Find: What cards do you have?

Since Belle answer that she sees all the five odd numbers from other players’ card excluding herself and Carol don’t have any odd number on her cards, that left you and Andy having all the five odd numbers.

The five odd numbers from 1 to 9 are 1 3 5 7 9. Deducting the cards that Andy has 1 3 7 would leave the two odd numbers 5 and 9, meaning, you have the cards 5 and 9.

Now only one left to identify. Looking back from the answer of Andy to the question card that he sees two or more values adding up to the same value from the cards of yours, Carol’s and Belle’s.

The sum of Belle’s card is 3 + 4 + 7 = 14

While the sum of Carol’s cards is 4 + 6 + 8 = 18

We can conclude from the results that Belle and Carol do not have the same value of cards. That left you and one of them who have the same value of cards.

We know that your other two cards are 5 and 9, letting x be your third card and x must be a number between 1 and 9, the sum of your cards would be 5 + 9 = 14 and adding the third card would make the same greater than 14. This would mean that you and Belle do not have the same value of cards and the one that’s left is Carol who has the sum of 18.

Subtracting the sum of Carol’s cards to the sum of the two odd number cards that you already know, we can get the last number of your card.

18 – 14 = 4

And so 4 is the other card that you have.

This means that the three cards that you have are 4 5 9

Answer to Question 2:

Find: What kind of logic will you use?

The logic that I use is “Process of elimination”, with more possibilities of being eliminated every time a new info comes up.

After Andy answered the question card, you would know that you have a total cards value of 14 (Belle) or 18 (Carol). Then Belle answered that she sees all of the five odd numbers from 1 to 9, and since Carol don’t have any odd number on her cards and you saw that Andy has the three of the odd numbers, so those numbers would be eliminated and the odd numbers left would be 5 and 9. This means that you have the numbers 5 and 9 on your cards. Since 5 plus 9 is equal to 14, the possibility of having the same total as of Belle would be eliminated, and so you can conclude that your total would be 18 (Carol) and from that you can get your last number by subtracting 14 to 18 which is equal to 4.