From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 15:45:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA19069 for ; Tue, 1 Dec 1998 15:45:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981201060918.6975.rocketmail@send104.yahoomail.com> Date: Mon, 30 Nov 1998 22:09:18 -0800 (PST) From: Han Wen Subject: Method for Solving the Professor's Cube (5x5x5) To: Cube Lovers Cc: Charles Lin , Keith Miller Hi, Okay, another so what, big deal. I finally solved the Professor's Cube. For those who may not be familiar, the Professor's Cube is a 5x5x5 Rubik's cube. Whew that was hard. It took me a good 4 days to figure out all the moves. Gees, it made the Megaminx seem like child's play in comparison. Once again, Noel Dillabough's Puzzler program was an invaluable tool to visualize and experiment with various moves. Thanks Noel! For those brave souls who would like to conquer this beast, the following solution may provide some enlightenment. It's a layers solution, in contrast to the corners-first solution that I have seen posted on various web sites. Good luck to you. The Professor's Cube is a truly challenging puzzle. ______________________________________________________ Method for Solving the Professor's Cube (5x5x5) I will use Noel Dillabough's system for referring to various slices or layers, as described in his Puzzler's F1 help. ________________________________________ Notation: U - The upper slice u - One slice away from the upper slice e - The equator slice d - One slice away from the lower slice D - The lower slice L - The leftmost slice l - One slice away from the leftmost slice m - The middle slice r - One slice away from the rightmost slice R - The rightmost slice F - The facing slice f - Once slice away from the facing slice M - The facing middle slice b - One slice away from the back face B - The back slice I will use the words "slice" and "layer" synonymously. A "face" is one of the six outer slices; namely, U, D, L, R, F or B. Rotations of the middle slices e, m or M will be in the same direction as the U, R and F faces, respectively. Let y denote one of the slices. y - represents a clockwise 1/4 turn of the y-slice y' - represents a counterclockwise 1/4 turn of the y-slice y2 - represents a clockwise 1/2 turn of the y-slice (For example, Rrm represents clockwise 1/4 turns using the RIGHT-hand of the R, r and m slices. Ll represents clockwise 1/4 turns using the LEFT-hand of the L and l slices.) Finally, let's consider the pieces or cubelets on any given face. There are four types of cubelets: corners, edges, centrals and a center. For a given face, there are 4 corners, 12 edges, 8 centrals and 1 center. With these four types and the intersection of any two slices using Dillabough's notation, we can specify the location of any cubelet. For example, consider the F-face: LU-corner: the corner cubelet on the upper left-hand corner of the F-face re-central: the central cubelet adjacent and to the right of the center cubelet of the F-face _______________________________________ First Layer (U slice): Solving the first layer is fairly straightforward. Basically the same as solving the Rubik's cube. The central pieces are the only thing really different. _______________________________________ Second Layer (u slice): 1. First, solve for the mid-central pieces (F-face mu, B-face mu, L-face Mu, R-face Mu). Get one of the mid-central piece on the same color face, and then rotate it into position by using the "free lane" from the opposite face. For example, let's say we want have a mid-central piece at the re position of the F-face. Use the D-"free lane" of the B face to position the mid-central piece without affecting your newly completed U slice, by moving: B2 U2 F' U2 B2. 2. Now, solve for the left and right central pieces (F-face lu, ru, L-face bu, fu, etc). Here's where we'll use a genuinely new move. Position one of the left/right central pieces on the D-face so that it and the position you want to move the cubelet into lie in the save vertical slice. For example, let's say we want to move the left central cubelet into the F-face lu position. Position the left central cubelet at the D-face lb position and perform the following u-layer DF Swing move: >From the D-face lb position: l d' l' d' l d2 l' See how that works? The corresponding move at the D-face rb position is: >From the D-face rb position: r' d r d r' d2 r This same concept is used to move the left/right central pieces into position for both the Second (u-slice) and Fourth (d-slice) layers. "Hey, what if my left/right central piece is on the F face? How do I move the piece to the D face so that I can apply this move?" Good question. Position the piece on the F-face ld or rd position and apply the corresponding move described above. That should move the cubelet to the D face where you can then apply the move again to move it into the correct left/right central position. 3. Finally, solve for the left and right edges (F-face and B-face Lu, Ru). Use the classic Rubik's cube move to rotate an D-edge piece into one of the middle layer edge positions. Namely, if the cubelet is at the F-face rD or lD position and the destination position is F-face Ru or Lu then perform the following: F-Edge Swing Moves: Destination position F-face Ru: D' R' D R F' R F R' Destination position F-face Lu: D L D' L' F L' F' L _______________________________________ Third Layer (e slice): 1. Solve for the left/right central pieces (F-face le, re, L-face be, fe, etc). You'll notice that the DF Swing moves will not work here. Darn. Instead, we'll use the F-Edge Swing move adapted for the l and r slices. Position the cubelet at the F-face md position then perform the following: F-Central Swing Moves: Destination position F-face Re: d'r'dD rR f'F' r fF r'R' Destination position F-face Le: d l d'D' l'L' fF l' f'F' lL "Hey, what if my left/right central piece is on the D face? How do I move the piece to the F face so that I can apply this move?" Same problem. Position the cubelet at the D-face rM position then apply the Re F-Central Swing move. 2. Solve for the left and right edges (F-face and B-face Le, Re). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face mD position and perform the following: e-Layer F-edge Swing Moves: Destination position F-face Re: D' R' D rR F' R F r'R' Destination position F-face Le: D L D' L'l' F L' F' Ll ______________________________________ Fourth Layer (d slice): 1. First, solve for the mid-central pieces (F-face md, B-face md, L-face Md, R-face Md). This is one of the most difficult steps. The mid-central pieces will be on either the d-slice or on the D-face. To move them into there correct positions, you'll need to use a few modified Rubik's cube moves: Place the D-face as the U-face when applying these moves: The following sets of cubelets are affected by these moves: cL = (central L-face Lu, edge U-face LM and central U-face lM) cR = (central R-face Ru, edge U-face RM and central U-face rM) cF = (central F-face mu, edge U-face mF and central U-face mf) Mid-central Tricycle: move: T2(U) = F2 f2 Uu Ll r'R' F2 f2 L'l' rR Uu F2 f2 action: Permutes the three sets of cubelets (cL, cR, cF) clockwise: Mid-central Bi-Flip Tricycle: move: S2(B) = L'l' rR bB Ll r'R' U2u2 L'l' rR Bb Ll r'R' action: Permutes the three sets of cubelets (cL, cR, cF) clockwise and flips the cR and cF sets. Let's clarify "flipping". Let's say for the cR set you have the colors: blue, (blue, yellow), yellow corresponding to the three cubelets. After flipping the cR set you'll have the colors: yellow, (yellow, blue), blue. Use these two moves to position all the mid-central pieces for the Fourth Layer. Now, if you're lucky, and Murphy's Law says that you will be, you may end up in a configuration where you'll have three of the mid-central pieces positioned properly, but the fourth mid-central position will be on the D-face. Okay, now we're going to start having fun. Position the central cubelet at the D-face lM position (i.e. on the left-hand side). Place the D-face as the U-face and then apply the following sequence of moves: S2(B) T2(U') U2 T2(U) S2(B') U' S2(B') Yes, all that trouble just to move one mid-central cubelet from the U-face to the F-face. 2. Whew, congratulate yourself if you've made it this far. Now, solve for the left/right central cubelets, (F-face ld, rd, L-face bd, fd, etc). Position the left central cubelet at the D-face lf or rf position and perform the following d-layer DF Swing move: >From the D-face lf position: l d l' d l d2 l' >From the D-face rf position: r' d' r d' r' d2 r 3. Solve for the left and right edges (F-face and B-face Ld, Rd). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face lD or rD position and perform the following: d-Layer F-edge Swing Moves: Destination position F-face Rd: D' R' D mrR F' R F m'r'R' Destination position F-face Ld: D L D' L'l'm F L' F' Llm' ______________________________________ Fifth Layer (D slice): 1. Solve for the corner cubelets using standard Rubik's cube moves. First, position the corners in their correct locations using the usual corner swappers: Adjacent corners swap: R' D' R F D F' R' D R D2 Diagonal corners swap: R' D' R F D2 F' R' D R D And then rotate or twist the corners in position using Sune's move: Sune's 3-corner twister: : R' D' R D' R' D2 R D2 2. Solve for the mid-edges (mF, RM, mB, LM) using a slight modification to the Tricycle moves. Place the D-face as the U-face when applying these moves: Mid-edge Tricycle: move: F2 U Ll r'R' F2 L'l' rR U F2 action: Permutes the three edges (LM, RM, mF) clockwise: Mid-edge Bi-Flip Tricycle: move: L'l' rR B Ll r'R' U2 L'l' rR B Ll r'R' action: Permutes the three edges (LM, RM, mF) clockwise and flips the RM and mF. 3. Solve for the left/right edges (lF,rF, Rf, Rb, lB, rB, Lf, Lb). Now, we're going to have some serious fun. The hardest part of this step is not getting lost while performing the long sequence of moves. Also while spinning all these slices, another difficulty is preventing the cube from exploding and keeping the central pieces from twisting around. Again, place the D-face as the U-face with applying these collection of moves: LR-edge Tricycle: move: F2 U Lm'R' F2 L'mR U F2 action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise: LR-edge Bi-Flip Tricycle: move: L'mR B Lm'R' U2 L'mR B Lm'R' action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise and flips the Rf, Rb, lF and rF. To get those last remaining cubelets in place, a few more exotic moves are necessary: Definitions: T(x) = F2 U x F2 x' U F2 x1 = L r' R' x2 = L l R' x3 = L m' R' (T(x) is a generalized form of the Mid-edge Tricycle) X1 = T(x1) T(x1) T(x1) X2 = T(x2) T(x2) T(x2) X3 = T(x3) Name: Double pair F swap Description: Swap two pairs of edges: (lF - Lb) and (rF - Rb) Move: X2 X1 Name: Double pair F cross swap Description: Swap two pairs of edges: (lF -Lf ) and (rF -Rf ) Move: X1 X2 Name: Double pair R swap Description: Swap two pairs of edges: (Rb - Lf) and (Rf - lF) Move: X2 X1 X3 Name: Double pair R cross swap Decription: Swap two pairs of edges: (Rb - rF) and (Rf - Lb) Move: X1 X2 X3 Name: Double pair L swap Description: Swap two pairs of edges: (Lb - Rf) and (Lf - rF) Move: X3 X2 X1 Name: Double pair L cross swap Description: Swap two pairs of edges: (Lb - lF) and (Lf - Rb) Move: X3 X1 X2 Name: LRL-edge Bi-Flip Tricycle Description: Permutes (lF, Lf, Rf) edges clockwise and flip lF and Lf edges Move: X3 X1 Name: LLR-edge Bi-Flip Tricycle Description: Permutes (lF, Lb, Rb) edges clockwise and flip Lb and Rb edges Move: X1 X3 Name: RRL-edge Bi-Flip Tricycle Description: Permutes (rF, Lf, Rf) edges clockwise and flip Lf and Rf edges Move: X2 X3 Name: RLR-edge Bi-Flip Tricycle Description: Permutes (rF, Lb, Rb) edges clockwise and flip rF and Lb edges Move: X3 X2 With these collection of moves, you should be able to finish off the Professor's Cube! *Sigh* -Han- P.S. Thanks "Professor" Meffert. For those folks like myself who have wrestled and completed your 5x5x5 cube, we can only ask and plead, "What's Next?!!" :)