Building Dungeons with Mathematics! | Forum. If you can follow that, a 4D dungeon doesn't shift, but it is confusing as all heck.
As a lighter version: In the past, I created a dungeon that consisted of seventeen 20 by 20 by 20 rooms. There was a circular 10' wide door on each wall, floor and ceiling of each room. Each doorway appeared black, like a darkness spell, and was actually a portal to another pocket dimension (each room was a pocket dimension). Each room shifted color every 6 seconds (round) going through the following sequence: Black, Purple, Blue, Green, Yellow, Orange, Red, White. The rooms were numbered 1 to 17. PCs entered the dungeon through a door that led to room 1.
With the door that
you entered the room being 1, the opposite wall's door 6, the floor 2, the ceiling 5, the right wall 3, and the left wall 4, I was able to map out a way for each door and color to be mapped in a sequence to head to another room. I had an excel spreadsheet that charted out all the combinations for each room (there were 48 color/door combinations for each room, and 16 rooms with combinations for a total of 768 potential options. As you traveled through the rooms, there were traps, monsters (which had different recharge mechanics, and were often powered by magic stolen from your vigor, making them reflections of your power level), and clues to be found. There were also exits that could take you out of the dungeon, although the destinations were not great options. If you searched long enough you'd find the clues that would indicate that you had to bleed in a corner of each of the first 16 rooms to gain access to the 17th room - which was, a room that contained the MacGuffin the PCs needed (once you had blood in a corner of each room, the room you were in would flash quickly between all of the different colors for 6 seconds and any door would take you to room 17 ... but if you didn't go in a round, then you were back to square one). However, the walls absorbed the blood after 2 minutes (20 rounds), so you had to be quick and know the pattenr you wanted to follow.
It took the PCs 4 years in real world time to solve it. I was called a plethora of unsavory names, but I asured them (using in game clues) that there was a solution.
They gave up with the first party after two sessions in the dungeon. They came back to it with another party two years later. That party gave up at the end of the session, but came back several times and used powerful magic to further figure out the tricks of the dungeon. Once they figured it out they tried several times to execute on the design, but failed to plan ahead and ended up not being able to get all 16 rooms done within 20 rounds by any of the PCs. One of them took it home as homework to plot it out - and 6 months later they tried it again, with PCs about ready to retire, and beat it. The MacGuffin ended up being the hook I used for the next campaign main storyline.
That group doesn't play together anymore, but we still use reference to that dungeon as short hand for a thing that just can't be solved, but has to be.