Thanks to @Gareth and @GentlePurpleRain for the help with this puzzle! I feel bad about taking all the rep for the answer now. @GentlePurpleRain, if you receive an unexpected bounty at some point, remember this ;-)

I think this sort of thing tends to even out in the long run.

It may slightly favour people who are willing to post partial solutions. I am unbothered by this not only because I happen to be one of those people but also because I think posting partial solutions adds to the fun for everyone else.

@Randal'Thor I'm not too worried about it. If I really wanted the rep, I would have posted my "partial" solution as an answer. I am generally not one of those people who posts partial solutions.

@Randal'Thor I would suggest cleaning up your answer, though, to remove the initial guesses. Someone who comes by in a year to look at the puzzle won't care about that; they'll be more interested in the solution.

@GentlePurpleRain Good idea; edited.