Date: 15 January 1981 18:30 cst From: VaughanW.REFLECS at HI-Multics (Bill Vaughan) Subject: Weird Algorithm - spoiler warning? To: Cube-Lovers at MIT-MC On going through the old mail, I was a little surprised that nobody uses the same algorithm that I do to solve the cube. But since mine isn't terribly efficient, that's not much of a wonder. Anyway, here it is. 1. Do bottom edges. Honest to god. I put all the bottom edges on top by random dithering, then for each one, turn it so its attached side facie abuts the color-matching face cubie, then rotate that face 180o. That gets the bottom edges right, but random hacking is almost as easy... 2. Do middle edges. (Getting colors right) I only use two moves here. FR'F'R and R'FRF'. I pick a cubie that's on a top edge but belongs on a middle edge - put its side facie adjacent to the matching color face cubie (deja vu) and use FR'F'R if it has to rotate right-and-down, or R'FRF' if it has to rotate left-and-down. 3. Get top edges in correct places. Essentially as in Singmaster, but I use only one of two moves. Align top edges so either: all are OK (skip rest of this step) or one is OK and 3 are wrong. (if that's impossible, use one of this step's moves at random and restart step - guaranteed to work.) Now either FURU'R' or FRUR'U' can be used to get everything OK. 4. Flip top edges as required. I use two different moves for this according to whether adjacent or opposite edges need to be flipped. Opposite: let Q = "turn body-slicing slice 1 qtw clockwise as seen from right". Then 4(QU) 4(UQ) flips FU and BU. Adjacent: FR'F'R.RU'R'U.UF'U'F flips RF and UF - you must reorient the cube to do this on two U edges. (I like this move because of its symmetry and - somehow - completeness. It also rotates the corner cubies adjacent to the edge cubies that it flips.) 5. Get the corners right. Here I have some fun, but the basic moves are: 3(FR'F'R) = (LFU,RBU) (RFU,FRD); 3(FRF'R') which also does a double interchange - tho' it's asymmetrical and I don't use it much; and B'FR'F'RB which stirs 3 of the top 4 CW or CCW - I never remember because I just use it twice for the "wrong" direction. 6. Tumble any corners that need it. Usually not many because of the nice color flipping properties of 3(FR'F'R) -try it. My tumbling move is a monotwist 2(FR'F'R).L.2(R'FRF').L' -- or replace the L and L' with LL if necessary - sometimes it's nastier and you have to do it twice. I've never counted worst-case moves. The algorithm is based almost entirely on Singmaster's Y commutator, and once you get that into your finger bones, you hardly ever make a mistake. On the other hand, this algorithm is bad enough it hardly deserves a spoiler warning. Bill q