Ugh. Never mind about my last message: that’s a red herring, and an annoyance, that maybe happens once randomly? When I started thinking about it as a parity puzzle and dependencies it all fell into place. So here’s a full process, I think?
The crystal panels have three colors: blank/red/pink (and cycle through in that order).
When the panel is blank,
ROX has no effect.
When the panel is red,
ROX cycles the fluids through Amberix/Gilsap/Chroton.
When the panel is pink,
ROX cycles the flow through none/trickle/swift.
If you ROX, and a change happens, then the panel in the next clockwise room cycles color (blank/red/pink).
The solved state is all rooms with Chroton flowing swiftly.
counting parity for order dependencies
Is there a word for when there are three states instead of two? Maybe it’s a trinity puzzle.
OK. So draw out the state, and count how many
ROX commands you need to cycle it to the solved state. You don’t care about the color changes, just the flow and fluid changes. So if you have Amberix flowing slowly, you need three
ROX: Amberix to Gilsap to Chroton, and slowly to swiftly. Now you can look at the next room’s color and see which color it will be in when the current room is solved.
This gives you a bunch of order dependencies.
You also know that when one end of that chain is solved, the next room is a certain color. So you know that one property must be in the right state, and the other is still changeable.
full derivation of order
For me, when NW is solved, NE is blank. So NE must be solved first.
When NE is solved, SE is blank. So SE must be solved first.
When SE is solved, SW is red. So SW must end up in red/anything/swiftly when SE is solved. Remember that the color will cycle when you do the last step of SE, so it needs to be blank/anything/swiftly before? Except…that if you’ve seen the “sparks weirdly” effect, then SW will be pink, and you want pink/Chroton/anything instead.
When SW is solved, NW is pink. So NW must end up in pink/Chroton/anything.
So you have to solve SE, NE, then NW. And we know that SW must end up in red/?/swift when we solve SE.
So…we can partially solve SW, then solve the east side. Now we can
ROX SW as many times as we want, it won’t lock us out of the solution. So we can trivially solve NW (it’ll change the color in NE but not the solution, so that’s fine). And then we
ROX SW however many times we need until it’s solved.
tldr full solution
Starting at the SW room and working counter-clockwise, set each room to Chroton flowing swiftly. You’ll have to mess up the SW room at some point, but don’t worry, it will work out that it stops there: you shouldn’t have to mess up the SE room again.
So…yeah. I’ve changed my mind. This is such a good puzzle. If you just worked your way around backward setting each room, (minimally messing up earlier solutions to make that happen) you’d eventually find it purely by accident. I’m pretty sure that’s how I got there the first time. But if you try to solve it by hunting through the maze of states it’s a hard puzzle, and even when you start looking at the parity it’s still an interesting challenge. Pure evil. I love it.
Edit:: grr…forgot to account for the effect of
sparks weirdly. On the other hand, that makes the solution even simpler and now I’m really smacking myself for not seeing it…