Since I seem to be getting this question a lot lately: yes, I'm still alive! But I am writing a dissertation. (And waiting to hear back from places where I applied for jobs, but that is not an excuse because those applications are already out there.)
Here's a puzzle I heard a couple weeks ago. You have a 10-by-10 grid of lights. Some of them are on, some are off. You are allowed to make the following moves:
(a): you pick one of the lights which is the center of some 3-by-3 square (i. e. it is not on the edge of the grid) and switch all the lights in that 3-by-3 square (on becomes off, off becomes on).
(b): like in (a), but with a 5-by-5 square.
Is it possible to get from an arbitrary starting position to the all-off position?