Teach 180: Math League (Day 51)

One of the things I wish I had more time to do during my day is to solve math problems.  I am not talking about writing answer keys, but problems that I do not initially know how to solve.  Problems that are novel and interesting.  Today I was given one of those opportunities.

Each month a handful of students get to solve challenging problems with the PA Math League contest.  It is a contest that consists of 6 questions and students have 30 minutes to solve those questions.  They span a variety of areas of mathematics including number theory, probability, geometry, algebra and trigonometry.  It is very challenging to get a perfect score on this contest.  When I took this contest in high school as a student, I would typically get 2 or 3 questions correct.

After the contest today, I had one senior who wanted to work with me at the whiteboard after the contest was over.  Since I had not been working on the contest when the students were taking it, (I was helping a student from one of my classes) I was initially stumped by the problem.  We discussed ratios of area of similar figures and between the two of us we generated some equations that eventually led us to the correct answer.  Our lively chatter about the solution brightened my day and made me wish for more moments like this.

As I was driving home in the car tonight after an 8th grade parent night, I was struck with another idea about how to solve the problem!  Since not all students have taken this contest across the country yet, I'll hold off on posting the problem and my solution for now.  In addition, I have some ideas that I want to try out in an effort to generalize a solution.  Generalizing solutions is the pinnacle of solving a math problem. As Fermat once said with his generalization, "I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain."