Sally, Joe, Bob, Fred, and Mary all won a prize in the school lottery. One of them won $500; one of them $196; another won $48; another, $16; and another, $2. Each of the students won in a different month: February, March, September, October, and December. How much money did each student win and in what month?
Clues:
1. At least one of the winners' names begins with the same letter as his or her winning month.
2. The girls won a total less than $250 and more than $205
3. One of the people with the shortest names won the least and the other won the most.
4. Mary won the month before Joe.
5. One of the girls won just in time for Christmas shopping.
6. The March and September winners won the most.
7. Sally won more than Fred
After clue 1, we know that either Fred won in February, Sally won in September, or Mary won in March...or any combination of the above as long as at least one is true.
After clue 2, we know that one of Sally and Mary won the $196, and the other won either $48 or $16.
After clue 3, we know that Bob and Joe won $2 and $500, but no which one won which.
After clue 4, we know that Mary had to win in a month that is right before another winning month...February or September. At this point, we can eliminate the possibility from clue 1 of Mary winning in March, so either Fred won in February or Sally won in September.
After clue 5, since we know from clue 4 that Mary did not win in December, Sally won in December. Thus, since one of the people had to win in a month that started with the same letter as their name in clue 1, and it is not Sally or Mary, we know that Fred won in February. Since, in clue 4, we determined that Mary must have won in either February or September and only one person can win in a given month, Mary won in September. Thus, Joe won in October, since he was stated as winning the month after Mary in clue 4. This only leaves Bob without a winning month, and his month is the only one left, March.
Thus, we have completely determined the names and winning months. Now for the money. We knew from before that either Bob or Joe won 2 or 500. Now we read clue 6 which states that the March winner (Bob) and the September winner, (Mary) won the most. Since the two greatest amounts are 500 and 196 and we know that Bob had to have won either 500 or 2, then we now know that Bob won $500, so Mary won $196. This leaves the $2 winnings for Joe who we had known earlier either won $2 or $500...now that $500 is eliminated we know that Joe won the $2. This leaves $48 and $16 left as possible wins. Both 196+48 and 196+16 fall within the greater than 205 and less than 250 range for the girls so Sally could have either won $48 or $16. However, clue 7 reveals that Fred won less than Sally, so we know that Fred won $16 and Sally won $48.
In the logic above, I have reached the following solution:
Name Month Money Won
Fred Feb. $16
Sally Dec. $48
Mary Sept. $196
Joe Oct. $2
Bob Mar. $500
SOLUTION
