From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 18:13:16 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 SAA19716 for ; Mon, 23 Nov 1998 18:13:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981123071931.2655.rocketmail@send105.yahoomail.com> Date: Sun, 22 Nov 1998 23:19:31 -0800 (PST) From: Han Wen Subject: Method for Solving the Megaminx To: Cube-Lovers@ai.mit.edu Hi, Well, it took me a 2-3 days, but I finally solved the Megaminx. Whew. I know, big deal. It's been done.. many many times... over a decade ago. But, I thought some of the moves I found may of interest to some of the Megaminx aficionados out there. So, here it is, I apologize for its length: Solving the Megaminx faces 1-11 are fairly straightforward. Ironically, the larger number of faces makes it easier to solve than the Rubik's cube, because they provide a lot more "free lanes" to move pieces around. There's actually just one move you need to remember to solve these faces. It's the same move when solving the middle layer of the Rubik's cube, when you want to move edge pieces from the bottom layer to their respective position in the middle layer. Namely, D'R'DRF'RFR' Solving the last face, however, is another matter. The general strategy I followed is the same as some of the standard methods for solving the bottom layer of the Rubik's cube. Namely, I first solve the 5 corners, then I solve the 5 edge pieces. To solve the corners, I simply used Sune's move applied with slight modification to the Megaminx. For the remaining edge pieces, I had to develop moves that only moved the edge pieces around, while leaving the corners unchanged. Noel Dillabough's Puzzler program was an invaluable tool for helping me experiment with various edge moves. Anyways, the following are my notes describing some of the more useful moves I've found. I'm pretty sure they're not the most efficient method for solving the Megaminx, but they're the best I could come up with. ___________________________________________ Notation for Solving the Last Face corner pieces: F=Front Face, D=Lower Face, L=Left Face, R=Right Face The F and D faces are adjacent The last layer containing the corners you need to flip/permute should be positioned at the D-face ____________________________________________ Move for Solving the Last Face corner pieces: Name: Sune's Double-Swap Description: Sune's Rubik's Cube move applied to the Megaminx Number of pairs of corners swapped: 2 Number of corners twisted counterclockwise: 3 Move: R'D'RD'R'D'3R ____________________________________________ Strategy for Solving the Last Face corner pieces: - Position the corners - Twist the corners in place by applying Sune's Double-Swap move twice ============================================ Notation for Solving the Last Face edge pieces: F=Front Face, U=Upper Face, L=Left Face, R=Right Face The F and U faces are adjacent X= L'R U2 LR' F2 X'=L'R U'2 LR' F'2 X2= X X = (L'R U2 LR' F2) (L'R U2 LR' F2) Xa= L'R U2 LR' F'2 Y= LR' F2 L'R U2 The last layer containing the edges you need to flip/permute should be positioned as the F-face or the U-face depending on the move described below: _____________________________________________ Moves for Solving the Last Face edge pieces: Name: F Tricycle 1 Description: Permutes 3 adjacent edges clockwise on the lower left of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X'2)^2 Name: F Tricycle 2 Description: Permutes 3 adjacent edges clockwise on the upper half of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X2)^2 Name: U Tricycle 1 Description: Permutes 3 edges clockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F' X2 Y'2 F Name: U Tricycle 2 Description: Permutes 3 edges counterclockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F X'2 Y2 F' Name: Cross-country Tricycle Description: Permutes 3 edges across the U and F faces No. Edges permuted: 3 No. Edges flipped: 1 Move: (X2 X'2)^4 Name: U Bi-Flip 1 Description: Flips two opposite edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X'2)^3 Name: U Bi-Flip 2 Description: Flips two adjacent edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (X2 X2 X'2)^5 Name: Cross-country Bi-Flip Description: Flips two edges, one on the U-face, one on the F-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X2)^3 Name: "W"-Cycle Description: Permutes all edges on the F-face in a "W" pattern No. Edges permuted: 5 No. Edges flipped: 2 Move: (X2 X2 X'2)^2 Name: "Figure 8"-Cycle Description: Permutes all edges on the F-face in a "Figure 8" pattern No. Edges permuted: 5 No. Edges flipped: 4 Move: (X2 X2 X'2)^4 ____________________________________________ Strategy for Solving the Last Face edge pieces: - You should only need to use F Tricycle and the Bi-Flip moves to completely solve the edges. The F Tricycle move usually needs to be applied twice. If anything is vague/unclear please feel free to request clarification. -Han Wen-