Snowboarding at Eldora

Boarding Betty is in town to write an article on Eldora Ski Area for "Powder" magazine. You have been selected to give her a tour of the mountain. Unfortunately, Betty has limited time to spend here, but she does want to ride all the runs except those in the beginner area. Your task is to lead her down each of the following runs accessed by the Challenger and the Corona lifts.
Challenger Lift Corona Lift
Jolly Jug Jolly Jug Glades West Ridge
Powderhorn Challenge Mule Shoe
Psychopath Windmill Corona Traverse
Bonanza International Corona
Klondike Sunset Salto Glades
Hornblower Around The Horn  

Since Betty has limited time, and we know that the Challenger and Corona lifts aren't known for their speed, your task is to take her down each run while making the fewest number of trips back up the lifts.

1. In the space below, translate your copy of the Eldora ski map into a graph. What do the edges represent ? What do the vertices represent ?











2. Beginning and ending at the lodge, find a path that will take you down each run while minimizing the number of trips up the lifts. What is the fewest number of lift rides that you will need to take ?

3. How would you describe this type of path ?

4. Could a circuit be formed ? What physical problem would exist ?

5. Would a minimum spanning tree or shortest route algorithm be useful in this case? Explain why or why not ?

6. Describe the method that you used to find the fewest number of trips.
Generalize your method to help Betty as she visits other ski resorts.


The Discrete Mathematics Project