Killing Mind

Check out the finalists board at Brain Tower. After spending several days knocking off a few of the problems, I finally managed to complete all 25 levels and put my name up in lights. Judging by the names and websites of the other finalists, I might be one of the few native English speaking people to do so!

There were some terrific puzzles along the way, from all aspects of mathematics. And naturally, each one conjured up a bunch of patterns I hadn't recognised before, demanding more investigation than was necessary to find the answer. Makes it pretty easy to flitter away many hours.

There was one puzzle that stood out as the least well understood by me. Essentially it asked that given the roots of x^6 + x^3 + 1, what happens when you plug those roots into x^2 + x + 1 one at a time and add? Admittedly, my answer was an educated guess, and I still don't know a good way to prove it...

Thanks very much to Alex Brie for posting the challenge.