Answer to September 5, 2005 Problem of the Week

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