Peter Renzland's Minimalist Rubik's Cube Solution Method

This Minimalist Method uses only 2 Transforms: Corners (c) and Edge-Swap (es).
c swaps 2 corner pairs. We can use it to swap 2 corners, or to twist 2 or 3 corners.

Notation:

The Face positions are: (my) Right, Left, (far) Back, Front, Up, Down.
R means turn the Right face clockwise. [r] means turn the whole cube: RBLF == (R[u])4.
R2 means RR; R- means RRR. lfu is the left-front-up corner, and bd the back-down edge.

The Transforms (Sequence, Face-Turns, Effects, and Side-Effects):
c  R B R- B-  (4 turns) urf:bru:rfu drb:ldb:bdr swap 2 corner pairs  (3 Edges)
es (R2B2)3    (6 turns) ru-rd & bu-bd           swap 2  edge  pairs    (no SE)

Derivatives:

mcsl  D c D- R-             7 urb-fdr-bur drb:L swap 2 corners, twist 1 (3 Edges)
mcsr  D c D- R              7 urf-drb-fur urb:R swap 2 corners, twist 1 (3 Edges)
cc    c c                   8 ur:R db:L        twist 2 corner pairs     (3 Edges)
ccc   c c c                12 fur-bru brd-dlb   swap 2 corner pairs       (no SE)
mct3l cF2D2[R-]  cB2D2[R]  12 bur,bdr,bdl:L    twist 3 corners L        (4 Edges)
mct3r [R-]D2B2c- [R]D2F2c- 12 bur,bdr,bdl:R    twist 3 corners R        (4 Edges)
mct   cc B L- cc L B-      20 fur:L bdl:R      twist 2 corners          (3 Edges)
The Minimalist method:

1. Do the corners of 1 layer intuitively.
2. Swap corners with c or mcs.
3. Twist corners with cc, mct3, or mct.
4. Do the edges of 1 layer intuitively.
5. Do the remaining edges with es.

Notes:

To move an edge cubie, line it up opposite its target cubicle, properly oriented (down the back); line up a helper edge-pair (already matched, or both still random) alongside (down the right); apply es; invert (undo in reverse) the line-up turns.

NB: mcsl works because swapping two pairs of adjacent corners of a square, and rotating a quarter turn, is equivalent to swapping one diagonal pair. (In Square Dance terminology: Passthru + revolve left 1 place == Ladies Chain.)

NB: mct works because twisting two pairs, changing partners, and twisting again, is equivalent to twisting one pair: 1122 + 1212 = 2001 (mod 3). (Square dance terminology: 2 couples face each other. The top couple dancers each spin 1/3 to the right. The bottom couple each spin 1/3 left. The ladies change to the other gent, assuming their twisted direction, as if they had started out with that gent. Again, tops spin right and bottoms left. This leaves the top gent spun 1/3 left, the bottom gent 1/3 right, and the ladies are unspun.)

One might say that c, mcs, mct, mct3 are 4 transforms that must be memorized. But the turns other than c itself are merely hints on how to apply c to do certain tasks, similar to the setup-turns used to apply es. This method is minimalist, but difficult to apply -- not for beginners. (Square dance callers will find this easy.)

See also Peter Renzland's Simple Elegant Solution Method which uses 3 easy Transforms.

[ peter [at] dancing [dot] org ]