You are given an disassembled Rubik's cube (Detachable centers,corners and edges). You are then blindfolded. If you assemble the cube while being blindfolded. What is the probability that the cube you have assembled can be solved as a standard 3x3 Rubik's cube?
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1$\begingroup$ Very low; maybe you'd like to ask this on Math SE? It seems more mathematical about permutations than puzzling solutions. $\endgroup$– XetrovJun 3, 2017 at 14:25
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1 Answer
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The colours on the 8 corners pieces fully determines the colours scheme of the cube. Therefore you will need to place the centre piece to match that exact colour scheme, though it may be in any of the $24$ spatial orientations. There are $6!=720$ ways to place the centres, of which $24$ are correct, so the probability of putting the centres correct is $\frac{24}{6!} = \frac{1}{30}$.
It is well known that the probability of assembling the corners and edges to make a solvable cube is $\frac{1}{12}$ which is because you need to have the correct total edge orientation ($\frac{1}{2}$), the correct corner twist ($\frac{1}{3}$), and the correct permutation parity ($\frac{1}{2}$).
Putting this together, the probability you are looking for is $\frac{1}{12} \frac{1}{30} = \frac{1}{360}$, or about $0.2778\%$.
answered Jun 3, 2017 at 16:33