There’s a certain variety of puzzle that I’ve always been fond of, which I call “parity puzzles”: there’s some particular action you can take to affect the puzzle, and you can do this action as many times as you want without consequences, but doing it twice is the same as not doing it at all. Solving the puzzle means achieving your goal while also having the puzzle be in the right state for it.
For a quick example, imagine a room with a lever in it. Pulling the lever seals the door to that room, but opens a door somewhere else on the map. Pulling it again undoes that. So your goal is to have the lever be in the “pulled once” state, while not being sealed in yourself. That would be a parity puzzle.
(In mathematics, “parity” means whether a number is even or odd. There are also variations with more than two states, like the water temple in Ocarina of Time, where changing the water level three times is the same as not changing it at all.)
There’s one particular version of this, the “parity maze”, that I’ve seen a few times, most notably in Spellbreaker. I’m sure there must be a more common name for this that I could google, but I’m coming up empty! Hence this thread.
In a “parity maze”, the map is bipartite: you can color every room either black or white, such that every time you move, you swap colors. (Imagine a chessboard, where you can only move horizontally and vertically, not diagonally. Every move would take you from white to black or black to white.) You’re pursuing someone or something, but they’re on the opposite color from you and move at the same speed, which means you can never catch them—until you find some clever way to move from white to white or black to black, and now you’re on the same color as your target.
Does anyone know other examples of this, or a more general name for them?
The only other example I’ve seen of this is the aliens catching the pigs puzzle. But I guess that’s not a great name… I think I’d understand “parity maze” too.
Not precisely what you’re talking about, but what this conjured out of my disused memories are the handheld electronic games from the '80s Merlin and Lights Out (Merlin had multiple games, one of which was basically the same as Lights Out on a smaller grid).
Basically you have a grid of lights. At the start of the game some are lit and some are unlit. pressing a light toggles the adjacent lights. The goal is to turn all of the lights off.
I don’t know if there’s a general term of this specific version of the puzzle (which I’ve seen many times in various guises in video games)
True that. I distinctly recall such a puzzle in the seventh guest where the player had to close all nine coffins by opening/closing them (triggering some neighbors to open/close as well). I have a similar puzzle in my WIP with slightly different rules (but the idea is the same).
I was so going to mention Merlin but didn’t think it would relate!
Merlin called it “Magic Square” and you had nine lights. The goal was a make a square - all lights except the center lit.
I figured out the trick somehow - if the lit pattern was uneven you would take note of which lights were on or which lights were off, and press all of those, ignoring how each press changed individual lights. Eventually doing that enough times would get the lights into a symmetrical pattern that was easy to change to the square.
Here’s an online version: it works just like I remember: Magic Square Puzzle
A wider category that includes all these puzzles and more is the ones that reduce to solving systems of equations in a finite field, typically modulo 2 (the “parity” bit). Lights Out is one of these, as are Sam Loyd’s 14-15 Puzzle (and most standard sliding blocks by extension), Berkelamp’s Switching, and many others. I don’t think there is a name for them because the taxonomies normally considered in game theory are different from the ones in recreational maths. In fact “Parity puzzles” is as good a name as any, and better than most.
Some creative uses of these puzzles in IF are known. In Zork: Grand Inquisitor, there is a puzzle of this type where the player is expected to flip some switches. It so happens that the puzzle is impossible to solve, and the player is expected instead to use magic to bypass it. This is a feature, as not all puzzles of this type need have a solution, depending on the initial configuration. The player is misled into thinking otherwise and forget that magic is useable in this situation.
I think I’ve said before that my favorite broad categories of classic IF puzzles are:
Parity puzzles like these ones!
Restricted passage: you can go a certain way, but not with all your gear, so you have to figure out a different way to get your gear to the other side. Could technically be thought of as a parity puzzle where the state-flipping action is “drop all your gear to go through the passage”.
Locked door: you can’t take a certain action until you have a particular item or piece of information, like a key for a lock.
I have a pet theory, based on my reading All the Adventures, that one mark of a good classic-IF development system is how well it supports parity puzzles and restricted passages. Basically every system can handle locked doors, but those are also generally pretty straightforward. Parity puzzles require you to experiment with the system and understands how it works so you can exploit it, and that’s another step up in complexity.
Yeah, I think most of the Zelda Water Temple-style puzzles are designed such that each togglable bit is controlled by exactly one toggle (or a set of toggles that each control exactly the same set of togglable widgets). While the distinctive hook of the Lights Out/Merlin version of the puzzle is that each toggable bit is flipped by multiple toggles and the toggles each control different sets of widgets.
You could argue that the former is just a degenerate case of the latter, but that way madness lies. Because wander down that garden path and you’ll end up with e.g. Hamiltonian paths, graph coloring, Chinese postman, the clique problem, and so on all being “the same problem” because a polytime reduction of any instance of one to an instance of any of the others is in principle possible.