Answer to May 14, 2001 Problem

The Four Student Problem

 
The Winchester Chamber of Commerce has invited one student from each of the four local high schools to attend a leadership luncheon. However, the Sherando student and the Handley student had just broken up and they did not want to sit next to each other.

In how many different ways could the students from Clarke, Handley, Sherando and James Wood be seated in a row so that the Handley and Sherando students do not sit next to each other?

 

Solution to Problem:

The answer is 12 different ways.

Letting C represent Clarke, J represent James Wood,
H represent Handley, and S represent Sherando,
I have listed the 12 possible ways in which the students could be seated with the Sherando and Handley students separated by at least one other student. (there are 4x3x2x1 = 24 different ways in which the four students could be seated if there are no constraints.)

C H J S
C S J H
J H C S
J S C H
H C J S
H C S J
H J C S
H J S C
S C J H
S C H J
S J C H
S J H C


Correctly solved by:

1. Richard K. Johnson La Jolla, California
2. Keith Mealy Cincinnati, Ohio
3. Walt Arrison Philadelphia, Pennsylvania
4. John C. Funk Ventura, California
5. Mary Fischer Joilet, Illinois
6. Joe Heintz Manchester, Tennessee
7. Renata Sommerville Austin, Texas
8. Bob Hearn Winchester, Virginia
9. Evelyne Stalzer New Jersey
10. ---------- United Kingdom
11. Bill Hall Wellington, Florida
12. Chip Schweikarth Winchester, Virginia
13. George Gaither Winchester, Virginia
14. David Powell Winchester, Virginia
15. Jason Farmer Winchester, Virginia
16. Joe Vance Winchester, Virginia
17. Ricki Stern Highland Park, New Jersey
18. Erin McGinnis Winchester, Virginia
19. Kirstine Wynn Winchester, Virginia
20. Gusti Oggenfuss Montet, Switzerland
21. David Dixon Bennettsville, South Carolina