A cube has6 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. ThepositionsareRight Left Up Down Front Back. ThecoloursareRed Orange Yellow White Green Blue. Thebasic 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]