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Cube visitors since 2004-March-26:

My Megaminx Solution

Before you delve into the solution that follows, be warned that for now, the solution is somewhat lengthy and completely textual (aside from a reference image showing the color orientation of my megaminx). Also, this solution is not for the beginner cubist. It assumes a general knowledge of a “CFL” (cross, F2L, LL - any style) cubing solution and the ability to do basic destructive/reconstructive moves. One day, I hope to add pictures and a more standardized notation (of which there is none at the moment), as well as beginner information, but this is how it stands for now:

Solving a 12-color megaminx
- Overview -
There is a difference between the methods and difficulties presented by the 12-color and 6-color varieties of the megaminx (aka “minx”). Since I only own a 12-color minx (and that’s all I’ve described how to solve to date), I’m going to concentrate on that. This solution can be used for a 6-color minx, but is not complete (since a parity problem can arise on a 6-color puzzle), and may not be the best approach.

This picture shows the color orientation of my minx. It’s important, because when I solve it, I always go through the colors in the same order - when I don’t, it slows me down significantly. Color Orientation Display The order I do them in is: red, dark blue, dark green, purple, dark pink together with brown, and finally light green (which also finishes the other 5 faces, light blue, white, yellow, light pink, and orange). You might expect that this would be a bad idea (perhaps starting instead with whatever face can be done in the fewest moves), but I found that I was losing most of my time during the solution trying to find pieces, so I opted for quick color recognition and location.

A while ago, I started with dark green, because it’s surrounded by dark colors. That way, I could look at a corner and tell where it went - top face (has dark green), northern “equatorial” line (across one edge piece from the green face, has two dark colors and one light), southern “equatorial” line (across one edge piece from the light green face, has two light colors and one dark), or bottom face (has light green). This worked well, but dark green didn’t really catch my eye very well, so the first face took more searching time than I wanted it to.

To minimize this, I now start with the dark color that seems to stick out the most to me (red), followed by the second most obvious which is also adjacent to the first (dark blue). Then, I go to the dark green face (which is mostly complete at that point), and proceed as I used to. So, after doing the dark green, I do the other 3 dark colored faces surrounding it, which leaves light green and the other light colors for the LL. There may actually be a better order, but because of how I used to do it, changing the color of the LL would set me back for quite a while until I’m used to the new order. I’ve decided that, for now, it’s not worth the downtime of relearning.

- Notation -
Though there isn’t really any standardized notation when talking about the megaminx, this is what I’ve come up with. I like it, because it makes sense to me, and so far I haven’t seen any ideas that are more understandable and straightforward than this. The faces are defined by the usual 6 letters used in cubing lingo Up, Down, Left, Right, Front, and Back.

Obviously, if this is the case, there can’t just be one letter per face, since there are twice as many faces on the megaminx as there are on a cube. I ended up with 6 faces defined by one letter (U, D, L, R, F, and B), 2 faces defined by 2 letters (BL and BR), and 4 faces defined by 3 letters (DFL, DFR, DBL, and DBR). Starting from an obvious U face (facing straight up), and an edge toward you (not a corner), F is adjacent to U, along with L and R to either side of it. The other two faces adjacent to U are BL and BR, next to L and R, respectively. B is the face directly opposite F, and D is directly opposite U. The remaining four faces are all adjacent to D (thus their first letter), and the second and third letters indicate the other two single letter faces to which they are adjacent. For example, DFR is adjacent to D, F, and R.

This causes another complexity, because edges and corners are denoted by the faces on which they reside. You can’t just look at a sequence of letters and determine which type of piece is being referred to by seeing how many letters there are. To simplify things a little bit, I separate the face definitions in a piece name with /’s. For example, the edge at the front of the U face would be U/F. While I could just write things like UBLBR (which would be the corner at the intersection of the U, BL, and BR faces), I think that would just get too confusing.

Finally, since there are 5 positions for each face, I had to do something different than the typical F, F', F2 move notation as well. Going back to the cube notation I originally learned from, I decided to use “+” for clockwise rotations and “-” for counterclockwise rotations. Two “clicks” in either direction is denoted with two of the appropriate symbol (e.g. F++ means turn F two clicks clockwise).

- First Four Faces -
When solving a face, I’m actually solving to 2 “layers” at a time - the face and the edges adjacent to it. First, put together a star of your preferred color, as you would do a cross for a 3x3x3 cube. I don’t know about optimal solving, but this usually seems to take me about 11-14 moves. To finish off the first face, insert 5 corner edge pairs. To do this, I don’t use a typical F2L approach...

Assuming the star is on U, find a corner that belongs on U, and put it on D (with the U color on D). Try to use a corner that can be moved to D with the correct orientation in just 1-2 moves (i.e. it is not on the U face). Next, find the edge that goes next to it and move it to a position next to D, so that rotating D will properly align the two pieces. Be sure to move D as needed to avoid reorienting or moving the corner off of D. After lining them up with a turn of D, they never come apart again. Unless they’re already in the right spot (two correct positions out of five possibilities), rotate the pair onto D and rotate D to position the pair across a face from the position they belong in. Finally, a simple R' D2 R type of move will insert them (R and D not referring to minx faces, of course). Repeat this until all corner edge pairs are in place - if any corners or edges are already in position, then you can use typical cube F2L algorithms or open slots to insert the other piece of the pair.

After completing the first face, complete a second and third face in the same manner as the first:
  1. Complete the star (add 2 edges for face 2 and 1 edge for face 3)
  2. Insert corner edge pairs, using the same technique as outlined for the first face
Make sure you don’t mess up any completed faces as you’re progressing, and also be sure to make the first three faces share a corner (i.e. all three are adjacent to each of the other two). The fourth face (adjacent to 2 of the first 3 faces) is done in a similar manner, except that the two corner edge pairs are put together on an adjacent face (since the opposite face is partially solved at this point) and some of the regular F2L algs are thrown into the mix more regularly.

Note: During these first few faces, I used U and D for ease of explanation, but I actually tend to hold the star to the lower-back-left (as I do with the cross on a cube), with the scrambled portions of the puzzle facing up and forward (toward me!) so I can more easily search for pieces. If you’re used to solving the cube with the cross on the bottom, you may do best with the star on the bottom of your megaminx, as well. With this puzzle, it seems to be all about minimizing search time, while the actual speed of your moves is a secondary issue for speed solving.

- The Next Two Faces (or getting to the LL)-
Once you get to this point, the megaminx should be completely solved, except for two faces which are still completely scrambled (aside from rare, lucky cases). I hold the minx with one scrambled face up (U) and one to the right (R). This way I can move U, R, F, and BR with the right hand and hold the puzzle with the left.

First, put together the U/L/BL corner with the two surrounding edges. I do this in three steps:
  1. Put U/L and U/BL on U, correctly oriented, positions reversed
  2. Using only moves of U and R, intuitively match the corner to one of the edges, keeping the other edge on U
  3. Still using only U and R, remove the pair from U, turn U, and replace the pair, so that all three pieces are matched up
If you’re familiar with cubing, you should be able to think through these steps on your own. If you can’t, then you’ll just have to wait for me to put up a beginner’s method to the megaminx - which should come some time this decade ;-)

After those three are matched up, turn them into place, and complete this step by inserting two corner edge pairs with typical F2L algs. Note that some cube algs will not work exactly, but with some “tweaking” may work on the megaminx. For some cases, you may have to use less than optimal F2L algs as a replacement for your usual cube F2L algs.

- The Last Layer -
This is where it gets interesting - I think a fair amount of people that know how to solve a 3x3x3 cube get this far on the megaminx, but not further, without learning someone else’s solution. I do the LL (last face, really) in four steps:
  1. Orient Edges (OE) - One look, using any of 3 algorithms
  2. Permute Edges (PE) - One looks, using any of 5 algs
  3. Orient Corners (OC) - One to two looks, with 8 algs
  4. Permute Corners (PC) - Not really using algs, each is placed individually
The following is a complete listing of the algorithms I currently use for the LL (holding LL on U).

OE algs:
  • 2 adjacent edges (U/F and U/R) need to flip:
    F+ U+ R+ U- R- F-
  • 2 non-adjacent edges (U/F and U/BR) need to flip:
    F+ R+ U+ R- U- F-
  • 4 edges need to flip (all except U/F):
    R+ BR+ BL+ U+ BL- U+ BR- U-- R-
PE algs:
  • Rotate 3 adjacent edges clockwise (U/R -> U/BL -> U/BR):
    (R+ U++) (R- U-) (R+ U- R-)
  • Rotate 3 adjacent edges counterclockwise (U/R ->U/BR -> U/BL):
    (R+ U+) (R- U+) (R+ U-- R-)
  • Rotate 3 non-adjacent edges clockwise (U/R -> U/BR -> U/L):
    (R+ U+) (R- U++) (R+ U++ R-)
  • Rotate 3 non-adjacent edges counterclockwise (U/R -> U/L -> U/BL):
    (R+ U--) (R- U-) (R+ U-- R-)
  • Swap an adjacent pair, and a non-adjacent pair of edges (U/R <-> U/L and U/BR <-> U/BL):
    (R+ U+) (R- U+) (R+ U-) (R- U++) (R+ U++ R-)
OC algs:
  • 2 adjacent corners - Rotate U/F/L counterclockwise (CC) and U/F/R clockwise (C):
    L- (R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) L+
  • 2 adjacent corners - Rotate U/F/R C and U/R/BR CC:
    (R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) (Note - this is the same as the previous alg without the L turns)
  • 2 non-adjacent corners - Rotate U/F/L CC and U/R/BR C:
    (R- F+) (R+ BR-) (R- F-) (R+ BR+)
  • 2 non-adjacent corners - Rotate U/F/L C and U/R/BR CC:
    R- (F- L-) (F+ R+) (F- L+ F+)
  • 3 adjacent corners - Rotate U/F/L, U/F/R, and U/R/BR CC:
    (R- U+) (L+ U-) (R+ U+) (L- U-) (last U- only necessary for edge realignment)
  • 3 adjacent corners - Rotate U/F/L, U/F/R, and U/L/BL C:
    (L+ U-) (R- U+) (L- U-) (R+ U+) (again, last U+ only necessary for edge realignment)
  • 3 non-adjacent corners - Rotate U/F/L, U/F/R, and U/BL/BR C:
    L- (BL- BR-) (R+ BR+) (BL+ BR-) (R- BR+) L+
  • 3 non-adjacent corners - Rotate U/F/L, U/L/BL, and U/R/BR CC:
    F+ (R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) F-
  • 4 or 5 corners - use one of the above algs so that only 2-3 corners remain mixed. Then fix those with the appropriate alg from above. There are algs for these situations, but I haven’t learned any yet.
PC Approach:
Finally, we come to corner permutation, which completes the puzzle. I do this in a way similar to Mark Jaey’s simple solution for the 3x3x3 cube. At this point, you will have anywhere from 3 - 5 corners that are incorrectly placed (or they are all correct in fairly lucky cases). To permute corners, start with the LL on U, and repeat these steps:
  1. Rotate U to put a corner in U/F/R that is not correct (or just rotate the puzzle the first time)
  2. Look at the colors on the F and R faces of the U/F/R corner - remember them
  3. Perform R- DFR+ R+ (or R- DFR- R+)
  4. Turn U until the edges on U/F and U/R match the corner that was removed from U in #3
  5. If the corner in U/F/R is a LL corner, repeat from #2, reversing the direction of the DFR turn in #3
  6. If the corner in U/F/R is not a LL corner, do #3, reversing the DFR turn.
  7. If the LL is solved (align with a U turn if necessary first), you’re done. If not (therefore swapping two pairs of corners), repeat from #1, again reversing the direction of the DFR turn in #3
Congratulations! You’ve solved your megaminx! Now, it’s just a matter of lots of practice which will also help to work in your puzzle.

- Additional Tips -
Beyond having a solid set of algs in your head and moving quickly, here’s a few things that should help you on your way to speed solving your minx:
  • If you haven’t yet, then lube your minx - they are normally very stiff, and a good lube will help. If you know how to take apart a Rubik’s brand 3x3x3 cube (springs under the centers, pop out an edge), then you should be able to get your megaminx apart as well.
  • Consider doing the colors in a specific order, so that you get used to it, and are looking for more obvious colors when there’s more to look through
  • Count your moves - I’ve counted a few times lately, and it’s always around 180 somewhere... I’d say with lucky and “bad” cases it’s probably always in the range of about 160 to 200 ([2004-May-11] Update: See table below for breakdown of solution moves/times). I know that’s a big range, but with so many possibilities for easy or hard cases, it can really vary.
  • Practice, practice, practice ;-) That’s obvious, I know, but it’s so true. Also, don’t worry so much about necessarily practicing just the megaminx. I’ve found that I can actually improve my megaminx times over a period of weeks when I never solve it once, and work instead on improving my cubing skills in general.
The following table shows, on average (over 5 solves), how many moves I use for each phase of the solution, as well as the percent of the total solution time spent to complete each phase. I further broke down each phase of the solution to its substeps, which can be seen in the larger table, below the initial summary table. In the summary table, the “Relative Speed” column is the ratio of the “% of Total Solution Moves” and “% of Total Solution Time” columns - higher numbers indicate a higher turn rate (moves / second):
Summary of Solution Steps
      # of Moves     % of Total Solution Moves     % of Total Solution Time     Relative Speed  
  Face 1     51.8     27.58%     34.80%     0.79  
  Face 2     28.6     15.23%     15.86%     0.96  
  Face 3     17.6     9.37%     9.65%     0.97  
  Face 4     18     9.58%     9.88%     0.97  
  Faces 5-6     28     14.91%     12.83%     1.16  
  Last Face     43.8     23.32%     16.98%     1.37  
  Total:     187.8    

Solution Steps - Detailed Breakdown
      # of Moves     % of Total Solution Time  
  Face 1     Star     13.4     10.20%  
  Corner/Edge Pair 1     8.6     5.95%  
  C/E Pair 2     7.6     4.86%  
  C/E Pair 3     7.4     4.24%  
  C/E Pair 4     7.4     4.62%  
  C/E Pair 5     7.4     4.94%  
  Face 2     Star     5.2     4.03%  
  C/E Pair 1     7.8     3.75%  
  C/E Pair 2     8.2     4.08%  
  C/E Pair 3     7.4     4.00%  
  Face 3     Star     2.6     2.43%  
  C/E Pair 1     7.4     3.60%  
  C/E Pair 2     7.6     3.63%  
  Face 4     Star     2.6     1.80%  
  C/E Pair 1     8.6     4.17%  
  C/E Pair 2     6.8     3.91%  
  Faces 5-6     C/E/E Trio     11.6     6.72%  
  C/E Pair 1     8.8     3.40%  
  C/E Pair 2     7.6     2.70%  
  Last Face     Orient Edges     7.2     3.14%  
  Permute Edges     7.6     3.46%  
  Orient Corners     10.8     4.34%  
  Permute Corners     18.2     6.04%  
  Total:     187.8    
Links to other Megaminx related resources (will open in a new window): If you have any specific questions about this solution, or suggestions for minor changes/corrections (major changes will have to wait for now), let me know!

Last modified: Sunday, 29-Apr-2007 15:11:31 PDT