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Date: Tue, 20 Apr 1999 08:58:14 +0200
To: cube-lovers@ai.mit.edu
From: Christ van Willegen
Subject: RE: Re : Re: Inventing your own techniques
At 15:13 19-4-1999 +0100, you wrote:
> The technique of solving the cube by use of commutators and conjugates
>is what most people worked out in the early days. However, I can testify
that
>it took us some time to realise that one could use second level commutation.
>That is, FRF'R' = [F,R] only affects seven pieces, but in fact it only
affects
>one piece in the L face, so taking the commutator with the L face produces a
>3-cycle of corners. Likewise [F,R]^2 only twists one corner in the L face
>and combining it with turns of L allows you to twist three corners the
same way
>or two corners opposite ways.
When I learned how to solve the cube (some 20 years back, I think...),
I was taught a layer-by-layer solution, consisting of 'modular' moves.
Most of the modularity occurs on the 3rd layer, namely:
- In flipping the edges, I use (RE)^4 to flip the UR edge. Then, I move
the top layer so that there's another edge to be flipped at the UR
position and I repeat the same procedure.
- In rotating the edges, I was taught the above-mentioned {R,F]^2 to
rotate an edge by 120 degrees. Later, I 'discovered' that [F,R]^2
does the same thing backward.
Most other layer-by-layer methods I've seen have formulas to flip 2
edges in the top layer, but you'll need two for the different confi-
gurations. Also, these methods mostly have two, three or more formulas
to rotate the edges in the toplayer, depending on configuration.
My method may not be the fastest around (it takes me about 2 minutes
to solve The Cube), but I don't need many formulas for it:
1st layer: on my own (make a cross, fill in the corners)
2nd layer: 2 formulas (standard layer 3 to layer 2 swing, two directions)
3rd layer: 4 (exchange edges, flip one edge, exchange corners, rotate
one corner)
Christ van Willegen