I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on an interesting math competition problem. This series was actually written by my friend Jeff Cagle, department head for mathematics at Chapelgate Christian Academy, as he tried technique after technique to solve this problem. I thought that his resolution to the problem was an excellent example of the process of mathematical problem-solving, and (with his permission) I am posting the process of his solution here. (For the record, I have no doubt that I would not have been able to solve this problem.)
Part 1: Statement of the problem.
Part 2: Initial thoughts on getting a handle on the problem.
Part 3: Initial insight.
Part 4: Geometric insight with a Riemann sphere.
Part 5: Roadblock.
Part 6: Getting past the roadblock.
Part 7: Insight.
Part 8: Proof of insight.
Part 9: Alternate solution (now that we know the answer).