April 12, 1999
Problem of the Week

City-County Track Meet




(1) Three teams -- Handley, James Wood, and Sherando -- compete in the City-County Track meet. The meet has ten events.

(2) Each event has one first place winner, one second place winner and one third place winner.

(3) Three points and a gold medal are awarded for each first place.
Two points and a silver medal are awarded for each second place.
One point and a bronze medal are awarded for each third place.

(4) Sherando wins more gold medals than either Handley or James Wood.

(5) The total number of medals won by Sherando is one more than James Wood's total and is two more than Handley's.

(6) Nevertheless, HANDLEY comes in first, with one point more than James Wood and two points more than Sherando.

(7) Determine the number of medals of each type won by each school.

  Gold
Mdls 		Silver
Mdls 		Bronze
Mdls 		Total
Mdls 		Total
Pts
Handley          
James Wood          
Sherando          



Solution to the Problem:

(1) Clue #4 gives us information about the gold medals:
Sherando > Handley and Sherando > Wood means that Sherando won at least 4 gold medals.

(2) Clue #5 gives us the following equation for total medals:
Sherando = Wood + 1 = Handley + 2

(3) Clue #6 gives us the following equation for total points:
Handley = Wood + 1 = Sherando + 2

(4) With 10 events, there must be 60 points, and from the previous statement, Handley scored 21, Wood 20, and Sherando 19.

(5) With ten events, there must be 30 medals, so Sherando got 11, Wood 10, and Handley 9.

(6) Now you should be able to fill in the table:

  Gold
Mdls 		Silver
Mdls 		Bronze
Mdls 		Total
Mdls 		Total
Pts
Handley 3 6 0 9 21
James Wood 3 4 3 10 20
Sherando 4 0 7 11 19




Correctly solved by:

1. Todd Lewis Winchester, VA
2. Dante DeFazio Winchester, VA
3. Jia Ran Rome, Italy
4. Jeremy Ramsey Stephens City, VA
5. Darren Rennie Winchester, VA
6. Bob Hearn Winchester, VA
7. Ginger Anderson Winchester, VA


Send any comments or questions to: David Pleacher