The next step is to figure out how to reverse generate conway's game of life. If you have previous game of life experience, you may already know how to do that. But I'm not a game of life expert. Its going to take quite a bit of research and trial and error to get that working. It will probably take me at least a day.
It all boils down to this: I don't want to waste two days of programming time for something as pointless as this. Especially since they could very easily say "sorry you're not a cultural fit" after spending all that time. Thats actually what happened to me a few months ago when I spent 4 days doing a programming problem for a job at reddit. They called me about a month later and had a 5 minute conversation with me, and then never heard from them agan. Assholes.
My new rule is that I don't spend any ore than a few hours on any one single problem, unless they pay me, or if it's interesting enough.
Also, this isn't as tough a challenge as you make it out to be: writing the game of life is, at most, a 2-hour assignment. So writing a game-of-life-reverser might tack on an extra 30 min. to hour. Then, you just hand-code in the gif into a game of life board, and run it through your reverser. Unless your gif is really large, in which case it might be a little more annoying, but probably not drastically so.
On the other hand, I once had a company give me a problem that was essentially to build a page that displays products from an API endpoint, and have that page infinitely scroll. That was something interesting, because infinite scroll is a useful skill. I had never implemented infinite scroll before, so in order to complete the task, I'd have to educate myself. And infinite scroll is a skill that I can use again. Conway's game of life in reverse is not a skill I'm ever going to use again, except for the next job interview busy work.
I'd probably have the same reaction to that as you did to the reverse-GOL. Sounds dreadfully boring, if that's the sort of stuff they do every day. I don't want to re-use old techniques over and over and over; I want to continuously discover new ones.
I would have done it, because it seems fun. And solving it proves that you know how to find libraries to do external stuff (reading/writing gifs. Knowing how to use basic ImageMagick or equivalent is a useful skill), and that you can solve some algorithmic task, or at least have an interest in it (no idea how hard reversing game of life is, or if this specific problem is bruteforcable, but if they ask it, I guess there's a solution).
[edit] Here's a cool page at wolframscience about testing for reversibility http://www.wolframscience.com/nksonline/page-1017a-text?firs...