July 23rd 2013

MAT 104

Professor's name

Zomorrodian Mohammad

Student's name

Donald Davies

1.

The salient fact about the problem is that in this set of playing cards, there are (10) cards

with numbers in a set of four (4) each. These numbers include 1, 2,3,4,5,6,7,8,9, and 10. There are four

people playing a guess game, Andy, Belle, Carol and myself.

Since Andy drew the first question card and was asked if can see two or more players whose cards sum

up to the same level, and his answer was yes.

Belle picked the next question card that asked how many different odd numbers he can see out of the

odd numbers. He said all of them. Andy suddenly declares that he knows what he has. He said 'I have a

1, a 5, and a7'.

Since no one can see their own cards, but can see the cards of the other three players, I was able to

know the cards I have based on the question cards Andy and Belle drew.

Solution

There are five even numbers and five odd numbers in this set of playing cards. The even numbers are

2,4,6,8,and 10. The odd numbers are 1, 3, 5, 7, and 9. Since Andy picked up a question card that asked

him if he can see two or more players whose cards sum up to to the same value, and he said yes.

I came to the conclusion that I have one of the set of cards that has the same value with another player's

cards.

I can see Andy's cards which summed up to 13, Belle has a total of 16 and Carol has a total of 12.

The second step was, belle was asked how many different odd numbers he can see, he answers

all. Since he could not see his own cards, and I can see his cards with the cards of the other two players.

I realized that the odd numbers that he can see were 1,5, and 7. there are 5 odd numbers therefore I was

able to know that I have a 3 and 9.

Since each player has a total of three cards, and I have two already that summed up to 12. With Andy

having a total of 13, Belle 16, and Carol 12, and none of them have cards that summed up to the same

value. I realized that the other card I have is 4 which will give me a total number of three cards and a
2.

total value of 16. Therefore the cards I have are 3,9 and 4. which is equal to 16, that answers the question that Andy drew.