I first became a member of the Mathematical Association of America in 1988. My mentor in high school gave me a one-year membership as a high school graduation present, and I’ve maintained my membership ever since. Most years, I’ve been a subscriber to three journals: The American Mathematical Monthly, Mathematics Magazine, and College Mathematics Journal.
A feature for each of these journals is the Problems/Solutions section. In a nutshell, readers devise and submit original problems in mathematics for other readers to solve; the editors usually allow readers to submit solutions for a few months after the problems are first published. Between the three journals, something like 120 problems are submitted annually by readers.
And, historically, I had absolutely no success in solving these problems. Said another way: over my first 30+ years as an MAA member, I went something like 0-for-4000 at solving these submitted problems. This gnawed at me for years, especially when I read the solutions offered by other readers, maybe a year after the problem originally appeared, and thought to myself, “Why didn’t I think of that?”
Well, to be perfectly honest, that’s still my usual. However, in the past couple of years, I actually managed to solve a handful of problems that appeared in Mathematics Magazine and College Mathematics Journal, to my great surprise and delight. I don’t know what happened. Maybe I’ve just got better at problem solving. Maybe solving the first one or two boosted my confidence. Maybe success breeds success. Maybe all the hard problems have already been printed and the journals’ editors have nothing left to publish except relatively easier problems.
In this short series, I’ll try to reconstruct my thought processes and flashes of inspiration that led to these solutions.
Mean Green Math 