![]() I still believe there are states solvable with only four visible faces, but I've not managed to find any correct example yet. (Edit: I missed out some edges that made my example state have at least three solutions, thereby invalidating my claim. There is no state solvable with only three visible faces, because for any choice of three faces, there will be at least two completely invisible edge cubies, the orientations of which are not uniquely determined. One such example is (L F2 L U B D2 U2 F' D' F' R2 D' U L'), where the U, F, L, R faces provide enough information to reconstruct the whole state. On the flip side, contrary to /u/DCarrier's answer, there are states that are solvable when four visible faces are given. The color arrangement is just similar to the 3×3 Rubik’s cube. ![]() (Alternatively, if we're allowed to continue looking at our n chosen face(s) during the solve itself, then the answer is simply n = 1, because we can always use preliminary moves to move every sticker into view to determine the identity of every piece.) This is a 2-layer mini Rubik’s cube, with only corner pieces. Each face of the cube has a different letter to show which way you need to face it. ![]() 2 Learn some notation so certain parts of this article are clear. Consider the superflip state where all twelve edges are flipped (L2 F' L2 R2 F L2 F' L2 B2 U2 L2 F' L R' U' R2 U2 B F' R' D' U') any choice of five faces would lead to the same situation as described above where the permutation of the edges on the unseen face is not uniquely determined. There are four similar center pieces on each face of the cube, four unique corner pieces, and 8 pairs of edge pieces (every two between corners are identical). In the former case, the answer is still n = 6. If every face but the U face is visible, it is indistinguishable from (L R F R2 U2 R2 U2 R2 U2 F' L' R'), where the four U edges are still flipped, but have also been rearranged. Consider the state given by (L' R F2 R2 D2 R2 B' R2 D2 R2 F2 L R' U'), where the four edges on the U face are flipped. Five faces do not suffice while any five faces would give enough information to determine all the corner cubies, this is not true for the edges. In the latter case, the answer is n = 6 (i.e. ![]() Do you mean "the smallest n such that for every legal Rubik's cube state, there exists n faces which provide enough information to determine a solution", or do you mean "the smallest n such that there exists n faces such that for every legal Rubik's cube state, these n faces provide enough information"? ![]()
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