This is the log of a dungeons and discourse adventure. I just read it myself, and even managed to figure out the curse without peeking at the solution. Happiness swells within me.
For those of you who enjoy philosophy and math, the log should be both amusing to read, and also give you a fun challenge to puzzle out the plot towards the end.
Enjoy.
http://lesswrong.com/lw/8kn/king_under_the_mountain_adventure_log_soundtrack/
Everyone is a genius. But if you judge a fish on its ability to climb a tree, it will live its whole life believing that it is stupid.
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Imagine you're in a room. This rooms contains six doors. One door on each wall, one hatch on the ceiling and one hatch on the floor. That means there are six other rooms surrounding you, just like this one. There's also an eight room which is two rooms over. And by "two rooms over", I mean "going two rooms in any direction to get you there". Going four rooms over, in any direction, will bring you back to the room you started from.
You're in a tesseract, a four-dimensional cube.
A tesseract is eight cubes balled up, just like a cube is six squares balled up. That does some funny things spatially; if you're in Room A for instance, and room B is right beside it, then both room A and room B have the same room directly above them. Same thing below, to the left, and to the right. Take the ceiling hatch from room A and you'lle come up through the floor in room C; take the ceiling hatch from room B and you'll fall out a wall hatch into the same room.
With me so far? Good. Now let's say there's a switch in the middle of every room, and pressing it completely changes all of the surrounding rooms. All eight rooms have switches like this in it, and every one brings you to a different tesseract (which is to say, that gives you access to 7 new rooms). Eight adjecent tessaracts, nine counting the one you start in, plus a tenth tesseract that can only be reached by switching over twice in a row.
40 rooms, 80 doors. Ten tesseracts balled up together.
Gentlemen, I want to run a dungeon in a 5-dimensional hypercube.