**Peter Renzland's Minimalist Rubik's Cube Solution Method **

This **Minimalist** Method uses only 2 Transforms: **C**orners (**c**) and **E**dge-**S**wap (**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) **R**ight, Left, (far) **B**ack, Front, **U**p, Down.

**R** means **turn** the **R**ight 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 **b**ack-**d**own 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 **c**F2D2[R-] **c**B2D2[R] 12 bur,bdr,bdl:L twist 3 corners L (4 Edges)
mct3r [R-]D2B2**c-** [R]D2F2**c-** 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
]