blgentry
Member
Most (all?) of us are aware that there are a variety of "illegal" positions on a nearly solved cube. A single rotated corner, for example, is not achievable by twisting the faces. Only disassembling the cube and reassembling it "wrong" can produce this, or any of the other "illegal states".
So I read on wikipedia that there are actually 12 different "cubie orbits" that account for these states. One of the 12 orbits is the one we all work with, which allows a fully solved cube; the other 11 will not yield a fully solved state. I got to wondering: Just how "wrong" will one of these orbits look when I try to solve the cube in the wrong orbit? Will I even be able to get it close?
I was cubing with a friend yesterday and we decided to try it. We both disassembled our cubes and reassembled them in a random configuration. Reassembling a cube, without having to look for the "right" pieces is SO much faster! Probably 30 to 40 seconds without really even trying.
We both finished assembly and solved. His came up fully solved with no pieces out of place. It was a one in 12 chance. Mine came up with (I think) one rotated corner and one flipped edge. Fixing that was very easy, as you can imagine.
We repeated the experiment a few times and always ended up with just a few things out of place. In thinking about it, I believe the worst case scenario is three things: One rotated corner, one flipped edge, and two swapped edges.
All in all, I find this process of reassembly far more satisfying. Instead of hunting down cubies, I just put it back together fast and then I get to do a solve.
I will never reassemble my cube "as solved" ever again.
Brian.
So I read on wikipedia that there are actually 12 different "cubie orbits" that account for these states. One of the 12 orbits is the one we all work with, which allows a fully solved cube; the other 11 will not yield a fully solved state. I got to wondering: Just how "wrong" will one of these orbits look when I try to solve the cube in the wrong orbit? Will I even be able to get it close?
I was cubing with a friend yesterday and we decided to try it. We both disassembled our cubes and reassembled them in a random configuration. Reassembling a cube, without having to look for the "right" pieces is SO much faster! Probably 30 to 40 seconds without really even trying.
We both finished assembly and solved. His came up fully solved with no pieces out of place. It was a one in 12 chance. Mine came up with (I think) one rotated corner and one flipped edge. Fixing that was very easy, as you can imagine.
We repeated the experiment a few times and always ended up with just a few things out of place. In thinking about it, I believe the worst case scenario is three things: One rotated corner, one flipped edge, and two swapped edges.
All in all, I find this process of reassembly far more satisfying. Instead of hunting down cubies, I just put it back together fast and then I get to do a solve.

I will never reassemble my cube "as solved" ever again.
Brian.