Problem of the Week
Hilton Memorial Lecture
Problem 3 (due Monday, March 16)
Recall that a $chord$ of a circle is a straight line segment whose endpoints both lie on the circle.
Several chords are drawn in a circle of radius 1 so that any diameter of the circle intersects at most $k$ of the chords. Prove that the sum of the lengths of all the chords drawn is less than $k\pi$.
Ashton Keith, a freshman majoring in math, is the only person who submitted a complete solution. His solution is very nice and different from our original solution. A solution along similar lines, but lacking sufficient details, was also submitted by Yuqiao Huang. Both our solution and the solution by Ashton Keith are discussed in the following link Solution