IRNjuggle28
Member
a) What's the probability that a random 2x2x2 position can be completely identified by only seeing the U, F, R, and L faces?
b) Same as a, but the 6 faces are a random permutation of the 6 colors.
c) How about on a 3x3x3?
d) How about on a 4x4x4?
I lack the knowledge to answer these, sadly. My thoughts for A are that the ones where it could be identified with UFRL are the ones where the UFR and UFL corners don't share any colors. If, for example, the blue/yellow/orange corner and the white/green/red corner were the two UF corners, other corners could be determined from only seeing two colors because, for example, if the DFL corner had blue on L and yellow on F, the other color has to be red because there are only two pieces with blue and yellow, and one of them already has all 3 colors visible on UFRL. The less variety of UFR and UFL colors, the harder it'll be to identify. It wouldn't shock me if the answer is 100% and I simply can't see how it would be done, though.
I doubt I said anything you don't already know.
B is stated a bit unclearly. Can you clarify what you're asking?
I have no idea about C. I feel confident that D is 0%, since the centers on B and D are completely undetectable, and could be in any configuration. Even if the cube looked completely solved only looking at UFRL, it could still be not solved.