Once you see those rules regarding M,S, and P trigger each other you can also see that either M-S-P or P-S-M has to appear. This isn't necessary to solve any of the games, but it might make them easier. I saw this right off the bat, for some reason, but I usually don't try to look for things like this because I waste too much time.
I'm far from an expert, just sharing my experience. =)