Answer to the Problem of the Week
for the week of September 5, 2005

The Cross Country Meet

Several schools competed in a cross country meet.   Each team sent three participants.

Erin, Katelyn, and Jessica were the three representatives for Handley.   Erin finished the race in the middle position, Katelyn finished after Erin in 19th position, and Jessica finished 28th.

How many schools took part in the race?

 

Solution to the Problem:

There are eleven schools.

As Erin finished in middle position we know that there must be an odd number of runners in the race, but because there are three girls representing each school, the number of runners must be an odd multiple of three.

In addition, we know that Jessica, who finished 28th, was not last, as there is an odd number of runners.   So there must be at least 29 runners.

If there were 33 runners, the middle position would be 17th.
If there were 39 runners, the middle position would be 20th.

However, we are told that Katelyn, who finished 19th, finished after Erin.

Hence there must have been 33 runners in the race and we deduce that eleven schools must have taken part.

Correctly solved by:

1. Walt Arrison Philadelphia, Pennsylvania
2. Britney White Columbus, Georgia
3. John Funk Ventura, California
4. Jeffrey Gaither University of Virginia
Charlottesville, Virginia
5. Rickard Jansson Tullängskolan, Örebro, Sweden
6. Tom Robb Winchester, Virginia
7. Chris Rogers Winchester, Virginia
8. Misty Carlisle Cornell University
Ithaca, New York
9. David and Judy Dixon Bennettsville, South Carolina
10. Charles Washington Winchester, Virginia
11. William Proffitt Winchester, Virginia
12. Erin Fennacy Fresno, California
13. Malin Fredriksson Tullängsskolan, Örebro, Sweden
14. Chris Jansson Tullängsskolan, Örebro, Sweden
15. Zaza Carlzon Tullangen, Örebro, Sweden
16. Gusti Oggenfuss Centre de Rencontre
Montet (Broye), Switzerland
17. Wictoria Widén Tullängsskolan, Örebro, Sweden
18. Richard Johnson La Jolla, California
19. James Alarie University of Michigan -- Flint
Flint, Michigan
20. Erika Skoglund Tullangen, Örebro, Sweden
21. Sagar Patel Columbus, Georgia
22. Tristan Collins Virginia Tech
Blacksburg, Virginia
23. Lina Peippo Tullängen, Örebro, Sweden
24. Bobby Arthur Winchester, Virginia
25. Marielle Clerissy Tullängen, Örebro, Sweden
26. Johan Honk-Walensjo Tullängen, Örebro, Sweden
27. Jim Arrison Norristown, Pennsylvania
28. Rachel Pridgen ----------
29. Austin Ball Columbus, Georgia
30. Joakim Olsson Tullängsskolan, Örebro, Sweden
31. Mattias Tyresgård Tullängsskolan, Örebro, Sweden
32. Krille Jansson Tullängsskolan, Örebro, Sweden
33. Gabrielle Groth Tullängsskolan, Örebro, Sweden
34. Magdalena Axelsson Tullängsskolan, Örebro, Sweden
35. Keith Mealy Cincinnati, Ohio
36. Matt Ahrnsbrak Winchester, Virginia
37. Julianne Harris Winchester, Virginia