A cube has 6 FACES, 8 CORNERS, and 12 EDGES.  You can refer to a face by naming
its position or its colour.  Cubes differ in their relative colour positions.
The positions are   Right  Left      Up      Down     Front  Back.
The colours are     Red    Orange    Yellow  White    Green  Blue.

The basic move, a q-turn, is a clockwise quarter turn of a face.  I normally
use {R,L,U,D,F,B} (or sometimes {R,O,Y,W,G,B}) to indicate a q-turn.  Thus,
"R" represents a clockwise quarter turn of the RIGHT face.   Half-turns and
counter-clockwise quarter-turns of the RIGHT face can be represented by "R2"
("big right"), and "R'" ("R prime" or "unright").  Similarly, using colours,
I like to write "R", "R2", and "R'" and say "red", "big red", and "unred".

Transformations -- Basic Tools

Try these out on a solved cube to get the idea of a transformation as a tool: Ta: (RBR'B')3 (short for RBR'B'RBR'B'RBR'B') "dual corner swapper" This swaps up-right and back-down corner pairs: ufr <-> ubr ; bdr <-> bdl You can use this to construct a "corner birotor": Tb: Ta F2 D2 [r'] Ta B2 D2 [r] ([r] means rotate entire cube cw about R-face) This rotates front-up-right corner left and back-up-right corner right.

These three are all you need to solve the cube:

T1: (RB)7R (RBRBRBRBRBRBRBR) -- swaps a pair of corners (scrambles edges) This (apparently) swaps front-up-left and front-down-left corners. T2: (R[u])12 (RBLFRBLFRBLF) -- rotates 3 corners right (scrambles edges) This rotates rbd, lbd, and lfd. T3: (R2B2)3 (R2B2R2B2R2B2) -- swaps 2 pairs of edges (no side-effects) This swaps ur with dr and ub with db.

How I solve the cube: (Takes 10 min when done slowly, forever if rushed.)

1. DO THE CORNERS OF 1 FACE. (By natural talent.) (Always align the centres.) 2. PLACE THE OTHER CORNERS. (Using T1, the "corner swapper") By rotating the opposite face, you can arrange it such that at most 2 corners are in the wrong POSITION. Use T1 to swap the 2 corners, if necessary. (What if the 2 corners to be swapped are not on the same edge but diagonally opposite? Easy: one q-turn will make them adjacent. Now do T1. Now undo the q-turn [having remembered what it was].) 3. ORIENT THE OTHER CORNERS. (Using T2, the "corner trirotor") If exactly 3 corners need to be rotated, place them at dfl, dbl, and dbr. Otherwise, put any corner requiring a right twist at "down front right", with the other three corners at dfl, dbl, and dbr. Do T2. Repeat step (3) until all the corners are done. (Remember: the centres are your friends) 4. DO THE EDGES. (Using T3, the "dual edge pair swapper") First pick a face (eg: white), and do its edges by natural talent. Now use T3 to do the next layer (the middle slice), remembering that WHITE is done already and I don't yet care about YELLOW (that's what's opposite white on MY cube). Now use T3 to do the last layer (YELLOW, on my cube). The procedure is always the same: Pick a CUBICLE that doesn't have its own CUBIE in it; find its cubie, Line up its cubie opposite the cubicle, PROPERLY ORIENTED. (now you have one pair that will be swapped.) Find another pair, to assist. (either both of a colour that you don't yet care about [yellow], or a properly opposite pair of a colour that's done already [white]), Place that pair alongside the first pair; now apply transformation T3, Undo the q-turns you did to place the pairs, in reverse order. (write down these q-turns at first, later you can just say them, and then just think them -- if you make a slip you'll have to start over.) I found {T1,T2,T3,Ta} because I'm right-handed and lazy. [1982]

Dancing.Org Peter Renzland Toronto (416) 323-1300 Peter@Dancing.Org