When I was a kid, I could not solve a Rubik’s Cube. I could solve one side, but where to go from there? Solving an adjacent side seemed like the right approach.
It is, in fact, the wrong approach. One method is to solve it by layers, which I learned to do a few years ago. Another method is to solve the edge pieces first, then solve the corners. I’ve been experimenting with this method, but it’s tricksy!
Yesterday, my neighbor’s autistic son asked me to solve his Rubik’s Cube. I did. Then he scrambled it and wanted to watch me solve it.
I solved one side.
Then he wanted me to solve, like I had wanted to when I was younger than he was, the adjacent side.
“That doesn’t work,” I said.
“Hard experience. I tried and I tried and I tried when I was younger, and it never, ever worked.”
So then I continued to solve the cube. At various points he wanted me to stop and leave it as it was, and then he wanted me to continue. Eventually, it was solved, and he later asked me where he should put it so that “other kids” couldn’t mess it up.
“Put it in a kitchen cabinet,” I said. “Up high, where only an adult can get to it.”
Yesterday evening, I decided to try to solve the adjacent side. The Cube is my fidget toy, basically. I have official 3×3 and 4×4 cubes at the office, and 3×3 and 4×4 speedcubes at home which, for work reasons, have been getting scrambled and solved several times a day of late.
With some experimentation, I was able to solve one side and then an adjacent side.
It is not efficient — you use all of the moves you would use to solve a Rubik’s Cube… without actually solving the thing.
All of the corners are in right right location, though two of them may need to be oriented. (In this picture, they were all oriented correctly.) Five edge pieces will probably be in the wrong locations and oriented incorrectly. With some work I can get the edges in the right locations, though not necessarily the right orientations.
This cube eventually I got to all pieces in the right place and two edge pieces flipped. And I don’t know how to flip them. The parity move I would use on the 4×4 cube to flip the edges doesn’t work on the 3×3 cube.
There is a solution. I don’t know it. But there is, and it looks like this could get me there.
So, neighbor’s son, I was wrong. You can solve the adjacent side. It is not impossible. But you don’t want to, because it’s a lot of unnecessary work.