Fifteen Handley students and fifteen Sherando students were competing for the fifteen spots on the Shenandoah Valley Math Team.

Since the students were equally qualified, the following plan was devised for choosing the team:

The thirty students would be placed in a circle, and starting the count from a specific student, every ninth person would be disqualified. The counting would continue until only 15 students were left and they would comprise the team.

Where should the fifteen Handley students stand so that all of them would be picked for the team?

Use H and S to represent the Handley and Sherando students and give the order of the 30 students beginning with the position of the first student to count off.


Solution:

This is known as The Josephus Problem in mathematics.
The order in which the students should stand is:

H H H H S S S S S H H S H H H S H S S H H S S S H S S H H S


Correctly solved by:

1. Geoff Keith Santa Monica, California
2. Walt Arrison Philadelphia, Pennsylvania
3. Christopher March Virginia Tech, Blacksburg, Virginia
4. Renata Sommerville Austin, Texas
5. Richard K. Johnson La Jolla, California
6. Rick Jones Kennett Square, Pennsylvania
7. Andrea Flandry Columbus, Georgia
8. Edgar Callaway Columbus, Georgia
9. Carter Staples Columbus, Georgia
10. Izzy Kushner Closter, New Jersey
11. Ashleigh Mark Columbus, Georgia
12. Ellen Sankovich Winchester, Virginia
13. David Powell Winchester, Virginia
14. Tori Eads Winchester, Virginia
15. Eric Harding Fort Collins, Colorado
16. Emily Moll Thiel College,
Greenville, Pennsylvania
17. Elizabeth Emmart Winchester, Virginia
18. Jill Schlueter Winchester, Virginia
19. Ghazaleh Joukar Winchester, Virginia
20. Bahareh Joukar Winchester, Virginia
21. Carter Wallace Columbus, Georgia
22. Robert Calhoun Columbus, Georgia
23. Emily Sparks Columbus, Georgia
24. Wilds Ogie Columbus, Georgia
25. Keith Mealy Cincinnati, Ohio
26. Jay Carpenter Winchester, Virginia
27. Janine Oliver Winchester, Virginia
28. George Gaither Winchester, Virginia
29. Ashley Maignan Columbus, Georgia
30. ---------- United Kingdom
31. Nick von Keller Winchester, Virginia
32. Brendan Jones Winchester, Virginia
33. Travis Riggs Winchester, Virginia
34. Mark Pennypacker Winchester, Virginia
35. Jaime Lockhart Winchester, Virginia
36. Steph Hower Winchester, Virginia