There are four public high schools located in the city of Fort Collins, Colorado. Students want to start at Poudre High school (at the corner of Overland Trail and LaPorte Avenue), travel to Rocky Mountain High (at the corner of Shields and Drake), then travel over to Fort Collins High School (at the corner of Horsetooth and Timberline), and then finally travel to Fossil Ridge High School (at the corner of Ziegler and Kechter).
How many different routes are possible if the students always travel SOUTH and EAST on the roads indicated in the diagram below?
Below is the actual map of our city:
Solution to the Problem:
The answer is 60 different paths that lead from Poudre HS to Rocky Mountain HS to Fort Collins HS to Fossil Ridge HS.
Use Pascal's Triangle to determine the number of ways that you can reach a particular intersection. In the diagram below, each number represents the number of different ways that you can get to that intersection (remember, you must always go south and east).
Correctly solved by:
| 1. David & Judy Dixon | Bennettsville, South Carolina |
| 2. John Funk | Ventura, California |
| 3. Luke Mansour |
Brookstone School Columbus, Georgia |
| 4. Mr. Robb's Discrete Math Class | John Handley High School Winchester, Virginia |
| 5. Tori Kennedy | Brookstone School Columbus, Georgia |
| 6. Elizabeth Lingo | Brookstone School Columbus, Georgia |
| 7. Tristan Collins |
Virginia Tech Blacksburg, Virginia |
| 8. Richard K. Johnson | La Jolla, California |