lemures said: Ok, I think I get this. She is using multiple dimensions: a a normal cube where the all red was on top, one where they are all on bottom, and so on and so forth. Then she decided to turn the dimensions so that this Nagato would have all the red sides. She basically borrowed them from the other 5 dimensions. Maybe?
Ummm, sort of. Not exactly. Almost. But not quite. :D What you (probably) think of as dimensions would be better termed "alternate universes", and while it is possible for her to solve the cube using other universes, if we want to bring dimensions into this, it gets a bit different.
Imagine it like this: there are many states the cube may be in, namely 42,252,003,274,489,856,000 possible states, which includes all possible legal configurations. Now, there are illegal configurations too, six of them (all sides of one color, every other configuration may be achieved by legal moves). All these possible states form three-dimensional cross-sections of a higher order form, the aforementioned n-dimensional probability-extension hypercube, and when you twist the cube, you are indirectly manipulating this form, to select a new state of the cube.
We, as residents of 3-space, see only the three-dimensional "cross-section" of the higher form that incorporates all possible configurations, and we can only manipulate this cross-section in three dimensions, so the configurations we can reach are limited, and limited by the mechanical structure of the mechanism. Nagato, on the other hand, can manipulate the higher order form, letting her bypass manipulating the cube by twisting the sides. What she does is she takes a look at the higher order "cube" (for lack of a better term), and manipulates that until she reaches the desired solution. Therefore, it is possible for her to select a state (ignorant of the rules) in which all sides are red, which is a possible state, even though it's illegal (there's a very small, but non-zero chance of it happening, so it's there among the possible configurations, which means she can select it). For her, that's simply the most efficient solution (in terms of time and number of moves), just like for me it would be to disassemble the cube, and reassemble the pieces into a solved configuration.
Did you remember to factor in the part where the three colors on the points and two colors on angles never adjust in relation to themselves (Ex: the three colors on one corner cannot be seperated,) Therefor limiting further combinations due to color-location relation? Also, due to said complexities of location-relation, only a single configuration, not counting simple rotations, in which the sides are each an individual color is actually feasible?
...Oh, you did. And then proceeded to bullshit it's significance from existence...
Oh, wait, you can't have it with more than 9 of any color on the block, though, if following standard color count, so don't forget to reduce the legal configurations to only ones that use exactly 9 of every color.
ThunderBird said: Ummm, sort of. Not exactly. Almost. But not quite. :D What you (probably) think of as dimensions would be better termed "alternate universes", and while it is possible for her to solve the cube using other universes, if we want to bring dimensions into this, it gets a bit different.
Imagine it like this: there are many states the cube may be in, namely 42,252,003,274,489,856,000 possible states, which includes all possible legal configurations. Now, there are illegal configurations too, six of them (all sides of one color, every other configuration may be achieved by legal moves). All these possible states form three-dimensional cross-sections of a higher order form, the aforementioned n-dimensional probability-extension hypercube, and when you twist the cube, you are indirectly manipulating this form, to select a new state of the cube.
We, as residents of 3-space, see only the three-dimensional "cross-section" of the higher form that incorporates all possible configurations, and we can only manipulate this cross-section in three dimensions, so the configurations we can reach are limited, and limited by the mechanical structure of the mechanism. Nagato, on the other hand, can manipulate the higher order form, letting her bypass manipulating the cube by twisting the sides. What she does is she takes a look at the higher order "cube" (for lack of a better term), and manipulates that until she reaches the desired solution. Therefore, it is possible for her to select a state (ignorant of the rules) in which all sides are red, which is a possible state, even though it's illegal (there's a very small, but non-zero chance of it happening, so it's there among the possible configurations, which means she can select it). For her, that's simply the most efficient solution (in terms of time and number of moves), just like for me it would be to disassemble the cube, and reassemble the pieces into a solved configuration.
