Imagine a cube-shaped building, with ten cube-shaped rooms along each side (10 rooms long, 10 high & 10 deep). Each cubular room has 4 walls, 1 ceiling and 1 floor. Each of the 6 interior surfaces in all 1000 cubular rooms is decorated with a different piece of art.
The rooms can be moved around the building, as if it were an enormous Rubik's cube, but they can also be spun on their axes, so all 6 walls of all 1000 cubes is capable of touching all the others (if the cube is so arranged).
How many combinations of art within the 'Cube Gallery' are possible? If you can run me through the workings of the maths I would be extra grateful. Also, what technical words/phrases/language are useful/interesting in expressing this concept? [more inside]
posted by 0bvious
on Apr 24, 2007 -