If I am given five faces of a rubik's cube, is it possible to
a) Determine if these are five sides of an actually solvable cube
b) Extend this to the sixth face in a unique way
Assuming one eliminated the obvious issues: Colour occurring twice on an edge or corner, opposite colours on the same edge or corner, or a repeated edge or corner. Would this guarantee that the cube can be extended to a solvable 6 face cube?
Asking out of curiousity but also because I was making a Rubik's cube cake and want to know if it would theoretically be solvable.
The answer to (b) is no. Start with a solved cube with yellow on the top. Then, flip all 4 edges on the yellow face. This is a solvable position. Call this position A.
Now swap the position of the two pairs of opposite edges on the yellow face. Call this position B.
Finally, remove the yellow face from A and B. The results are the same. So the extension is not unique.