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

Clue 1: We either have Sally in Sept, Fred in Feb or Mary in March.
Clue 2: Neither Sally nor Mary won $500 or $2. One must have won $196 and the other won either $48 or $16.
Clue 3: Bob and Joe won $500 and $2. Since we know $196 is taken by one of the girls, Fred either won $48 or $16.
Clue 4: Mary’s month was either Feb or Sept. Looking back at Clue 1, this means that we either have Sally in Sept or Fred in Feb. Also, Joe won in March or October.
Clue 5: I think this means one of the girls won in December (I wouldn’t call October "just in time" even though it is shopping season for some people). Since we know Mary can only be Feb or Sept, Sally must be December. Looking back at Clue 1 again, this means that Fred must be in February, leaving Mary in September, forcing Joe into October. By elimination, Bob won in March.

Feb Mar Sep Oct Dec
Frd Bob Mar Joe Sal

Clue 6: The March and Sept winners are Bob and Mary, and winning the most means they won $500 and $196. We already said the girls couldn’t win $500, so Mary won $196 and Bob won $500. Looking back at Clue 3, this means Joe won $2.

Feb Mar Sep Oct Dec
Frd Bob Mar Joe Sal
    500 196  2

Clue 7: The two amount of money left are $48 and $16. If Sally won more than Fred, then Sally won $48 and Fred won $16. Done!

Feb Mar Sep Oct Dec
Frd Bob Mar Joe Sal
16  500 196  2  48

Posted by nikki on 2005-01-27 14:45:01