From mouse@collatz.mcrcim.mcgill.edu Fri Dec 10 09:16:34 1993 Return-Path: Received: from Collatz.McRCIM.McGill.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA25485; Fri, 10 Dec 93 09:16:34 EST Received: from localhost (root@localhost) by 4504 on Collatz.McRCIM.McGill.EDU (8.6.4 Mouse 1.0) id JAA04504; Fri, 10 Dec 1993 09:16:29 -0500 Date: Fri, 10 Dec 1993 09:16:29 -0500 From: der Mouse Message-Id: <199312101416.JAA04504@Collatz.McRCIM.McGill.EDU> To: senya@rainbow.ldgo.columbia.edu Subject: Re: Needed: Basic elements of solving Rubic Cube: Cc: cube-lovers@ai.mit.edu > Subject: Needed: Basic elements of solving Rubic Cube: (Does anyone happen to know whether Ernö Rubik knows what's happened to his name? I don't mean just here, but how common a term it's become. And I apologize for using ö instead of what I think is the proper long accent, but Latin-1 doesn't have the proper one....) > Could you gentelmen suggest me the place where I can find the basic > (elementary) combinations to solve the cube? There are no *the* basic combinations. I would guess there are as many different sets of combinations as there are cube solvers. > Like the sequence to swap two "internal" side's boxes while not > changing the positions of all other "internal" boxes but probably > only rotating them? > Or could you tell me about the method to rotate some of edge elements > without swapping them? Well, for what it's worth, when I solve a cube, I do it as follows. (Slice turns: if I write FB, I mean turn the F-B slice in the direction one would turn F for an F turn, similarly for other slice turns: turn the slice as if it were carried along by the turn named by the first letter. Thus LR and RL are inverses. Is there some standard representation for slice turns?) - Solve one layer ad-hoc. (This refers to a layer of cubies, not just one face of the cube.) I often don't worry about edge flips at this stage. Some simple operators I use: To get corners in place: F D' F, or F' D F, depending on corner orientation. To get edges in place: If the cubie is on the D face, FB/BF/RL/LR, D/D', inverse of the slice turn. If it's on the middle layer, F/B/R/L, UD/DU, inverse of face turn. - Turn the cube so the solved face is L. Solve what then becomes the R-L slice layer with a combination of R2 U2 R2 U2 R2 U2, to move cubies around within the slice layer, and either of two sequences to move cubies between the R layer and the slice layer: R2 D R' B2 R2 B2 R2 B2 R' D' FB D R' B2 R2 B2 R2 B2 R' D' BF (The first one is a sequence that normally ends with R2, but since the R layer is scratch at this point I often don't bother.) These are, of course, interspersed with R, R2, and R' turns to get edges in the correct places for them. At this point you will have two layers solved, except possibly for some flipped edges. Next, corners of the "scratch" layer. Check them for placement, ignoring orientation. They can be: 1) All in place. This is the easy case. :-) 2) Two swapped. Make one quarter-turn to reach case 3. (They can't be diagonal, they must be adjacent - or some joker has taken your cube apart.) 3) One in place, other three permuted. 4) Two pairs, each swapped. If the swaps are diagonal, turn the layer a half-turn to reach case 1. In case 3 or 4, the corners can be put in place by holding the cube with the unsolved layer as U and repeating L F L' F' L F L' F' L F L' F' twice, turning U so as to place appropriate pairs of cubies in the UFL and UBL corners. To orient the corners correctly, hold the cube with the unsolved layer as F and use R B2 R' U' B2 U and its inverse U' B2 U R B2 R' with a turn of the F face in between; this will allow you to twist the corners into correct orientation. All that remains at this point is positioning the edges on the last layer, and possibly some edge flips. To position the edges, I normally use (with U as the unsolved layer) R2 D R' B2 R2 B2 R2 B2 R' D' R2 FB D R' B2 R2 B2 R2 B2 R' D' BF R2 U2 R2 U2 R2 U2 with appropriate turns of U in between, swapping the FR and BR edges repeatedly as auxiliaries while swapping pairs of edges on U to get them in place. (The difference between the first two sequences is that the first one swaps UB and UR, the second UB and RU.) Edge flips are all that's left at this point. Judicious choice of which of the two sequences above can often drastically reduce the work to be done here, but there's often some left anyway. The basic sequence I use for this is RL U RL U RL U RL U, which flips four edge cubies in-place: UB, UL, DB, and DF. (A similar sequence U RL U RL U RL U RL is similar but flips UR instead of UL; this can be thought of as U X U', where X is the first-given sequence.) My use of this sequence is usually ad-hoc; sequences such as X F X F' will let you flip arbitrary pairs of edges. Presto! You have a solved cube. :-) In practice, I often take shortcuts; for example, if X represents the R B2 R' U' B2 U sequence, then X B2 X B2 X B2 will twist three corners on B.... der Mouse mouse@collatz.mcrcim.mcgill.edu