Assignment 1 logic application In this paper I will summarize the salient facts of the "guess your card game" and explain my strategy in solving this problem. In doing so, I will respond to each player's comment and apply a strategy of process of elimination and logical deduction to establish new facts and reach conclusions.

First when Andy responds "yes" to the question "do you see two or more players whose cards sum the same value," this is revealing. The sum of Belle's cards equal 16 (5+4+7=16). Carols cards sum up to be 12 (2+4+6=12). Since Andy cannot see his own cards he obviously cannot factor his own cards into his conclusion. As a result of this, I can deduce that I must be holding cards that equal either 16 or 12. Next, after Belle draws her question card, "of the five odd numbers, how many different odd numbers do you see?" and proclaims that she see's "all of them." The game contains the numbers 1 through 9. This means that the five odd numbers are 1,3,5,7 and 9. Andy has 1, 5 and 7, Belle has 5,4 and 7 but cannot see her own cards, and Carol has 2,4 and 6. Out of the odd numbers, only Andy has any visible to Belle. Since Andy has 1, 5 and 7, but Belle claims she can see all odd numbers, this must mean I have 3 and 9. 3+9=12 and since I still have one unidentified card to add to my total, and my total equals either 12 or 16 that unidentified card must be a 4. Lastly, Andy knows what numbers he has right away based on the answer to the second question. Here is why. Since Belle claims she sees all odd numbers but the only odd numbers visible to Belle are my 3 and 9 and whatever Andy has, Andy can deduce that he must have 1, 5 and 7.