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I challenge everyone to come up with a (useful) commutator involving only exactly 2 faces (or layers) of the cube. The good ones i know use 3 faces or more

Per

Correction:

I actally know this one usng 2 layers: m D2 m' D2, in commmutator notation [m,D2]

To place the last few cubies on the last two centres of a 7x7x7 cube. Get as close as possible the normal way. And use these commutators to finish the job.

5x5 block of a 7x7 cube (both the same relative positions on front face and top face)

A A A B B
X C D X X
X X X X X
X X X X X
X X X X X

"A" move: A(up) U r U'
A(down) U r' U'

"B" move: A(up) U' l' U
A(down) U' l U

"C" move: A(up) U (Slice 5)(up) U'
A(down) U (Slice 5)(down) U'

"D" move: A(up) U (Slice 5)(up) U'
A(down) U (Slice 5)(down) U'

The positions marked "X" can be rotated on both the top and front face to get into the stated positions for the above commutators.

Very similar commutators for the 6x6 and 5x5 cube too, but just with slighty different slices to move.

I've been thinking about this, you can use (correct me if I'm wrong) [X,Y] as commutator, where X and Y are 2 random sequences using only 2 layers. You than have a commutator. Afterwards, you only have to specify what parts of the cube are affected by this.

I've been thinking about this, you can use (correct me if I'm wrong) [X,Y] as commutator, where X and Y are 2 random sequences using only 2 layers. You than have a commutator. Afterwards, you only have to specify what parts of the cube are affected by this.

I've been thinking about this, you can use (correct me if I'm wrong) [X,Y] as commutator, where X and Y are 2 random sequences using only 2 layers. You than have a commutator. Afterwards, you only have to specify what parts of the cube are affected by this.

That's indeed pretty much the definition which Per used in the challenge. But the challenge isn't to make a commutator with 2 sides, but making a useful commutator with 2 sides.

The problem is that it's not so easy to find something with 2 sides that affects little part of the cube. That's the whole challenge.

Half a minute is certainly not enough.
If you mean a commutator [X, Y], then the answer is: Yes, with a conjugation. But you probably wouldn't be happy with it, unless there's a neat comm I don't know about.

And of course , if you just want a 2-gen comm with the same net effect, that's easy.

Half a minute is certainly not enough.
If you mean a commutator [X, Y], then the answer is: Yes, with a conjugation. But you probably wouldn't be happy with it, unless there's a neat comm I don't know about.

And of course , if you just want a 2-gen comm with the same net effect, that's easy.