That's a fair point, and it would make sense to allow the same for the robot. That could mean that you can allow for preprogramming the layout before. Or you could put two cameras on the robot to take pictures of 5 of the sides. I believe you can infer the last side based on knowledge of the others.
In any case, given the fact that the human record for solving a cube is about 4.5 seconds, building a robot that can beat that would certainly be possible, but likely harder to do than the one from the article.
”I believe you can infer the last side based on knowledge of the others.”
Can you? If you flip all four edge pieces on the bottom face the bottom color shows up at all four side faces, and you wouldn’t be able to determine whether those four edge pieces got permuted, too.
Thinking a bit more about it, this problem already pops up if the bottom face has either:
- three edge pieces that share a color, with that color showing on the side.
- two pairs of edge pieces that share a color, with the twice shared colors showing on the side.
The first isn’t uncommon; if you pick three edges at random, the probability that they share a color is 1 * 6/11 * 2/10 = 6/55, and there are four ways to pick three edges from the bottom face, for (I think) a total probability of 24/55 - 4 * 6/55 * 1/9 (the probability that all four share the same color), or a probability of over 1/3 (if that seems high, consider the following: because of the pigeonhole principle, between the edges of any face of the cube there always is at least a pair sharing a color). That means that, even ignoring the second possibility, there’s at least a 1:24 probability of seeing this problem on a random cube.
Not all cube configurations are achievable by cube moves. That is, if you pull off one corner of a cube, rotate it, and stick it on again you get a cube which cannot be solved (except by disassembling it again).
I think it actually is possible to infer the sixth side of a cube if you can see the other 5, because only only one configuration of the remaining side is actually acheivable.
Quite. But we're talking about the permutation of the edge pieces on that face. You wouldn't be able to infer where they needed to be moved to if they were all just showing the bottom face colour.
In any case, given the fact that the human record for solving a cube is about 4.5 seconds, building a robot that can beat that would certainly be possible, but likely harder to do than the one from the article.