Thank you so much! I’ve been trying to get someone to help me for over a millennia!
The alien John said over the phone enthusiastically. You start wondering what you’ve got yourself into…
You have been asked by John to help him sell his house. And to be able to put it out for sale, you need to calculate its total floor area. You open the letter John sent, and find the following schematic:
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You’re a bit surprised that John seems to be living in the second dimension, that his house has no entrance, and all rooms seem to be open! But you don’t spend to much time dwelling on it, you are getting paid handsomely after all. After counting all open floor space, you send a message back to john specifying the livable area (in meters) in the drawing, and promptly get a response:
That doesn’t seem to be right, how in the world could livable area be specified in meters? It’s always in cubic meters!
You quickly realize your mistake. you forgot to use the dimensionality expanding glasses John sent you a while back! Hopefully it won’t be to hard of a mistake to correct.
Looking at the drawing with the glasses on, you magically see the coordinates of the hypercubes making out Johns house:
Download 4d House SchematicYou remember John telling you that gravity points down in the direction of the vector [1, 0, 0, 0] in his world. Now, what is the total cubic meter area of livable space in Johns house?