July 15–July 21, 2008
Problem
In Hughmoar County, residents are allowed to build a straight road between two homes as long as the new road is not perpendicular to any (even a non-intersecting) existing county road.
Amy, Bert, and Charles were the original residents; they lived at the corners of an equilateral triangle of side length 9 miles. They built three straight dirt roads along the sides of the triangle. Next, David built a house on the road between Amy and Charles, three miles away from Amy. Earl then built a house on the road between Bert and Charles. Two new straight roads soon were built, one between David and Bert, and another between Earl and Amy. A newcomer named Felton, who liked to be in the center of things, built his house on the intersection of these two new roads, and then made another new road straight from his house to Charles. He was promptly arrested for building a perpendicular road.
Where must Earl have built his house for this to have happened?
Solution
There were three possible answers: see a solution here.
List of solvers
One solution: Konrad Schroder, Melanie Terry, Steve Wilmarth (outside).
All the solutions: Dustin Moody, Jacob Lewis (graduate); Mike Goodman, Lloyd Sakazaki, Kate Smith (outside).
Kate Smith wins the prize!