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 |