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10/16/2007

January 8–January 14, 2008

Problem

Suppose ABC is a general triangle with area 1. Divide side AC into 4 equal parts and connect B (with straight lines) to each quarter of AC. Similarly, divide and side AB into 5 equal parts and connect each fifth back to point C. Let D be the point that is 1/5 of the way from A to B, and let F be the point 1/4 of the way from A to C, and let E be the intersection of CD and BF. What is the area of the quadrilateral ADEF?

triangle diagram

Solution

List of solvers

Steve Wilmarth (undergrad), Dustin Moody, Sean Holman, Alan Jamison, Travis Willse, Gary Raymond (graduate); Rich Bauer (alumni).

Steve Wilmarth wins the prize!