May 14, 2001
Problem of the Month

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 the 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

Send any comments or questions to: David Pleacher