The results are in for September and October!
For October, the winning submission of Rüdiger’s Rutabagas was joint work by T. Rhyker Bernandez and Nathan Thomas. The solution was the Catalan Numbers, and we can hardly give a better explanation than that found here. (The problem translates into counting rooted plane trees.) Check it out; you’ll see that tons of interesting problems have Catalan numbers as the solution. They should definitely be in your problem-solving toolkit.
We’ll announce the December winner soon, and return in February with a new problem!
Congratulations to all!