Thursday, May 26, 2011

4x4x4 Rubik's Revenge

The 4x4x4 Cube is the next step up from the Rubik's Cube. The basic idea is to reduce the cube so it's essentially the same as a 3x3x3 cube. Once that's done, it behaves like a 3x3x3 cube - with 1 or 2 possible exceptions.

I will be using the white-yellow, blue-green, red-orange colour scheme, with white on top, red on left and blue on right. It's assumed you can solve a 3x3x3 rubiks cube.


The Basic Plot

  1. Solve centers
  2. Pair edge pieces
  3. Position edge pairs
  4. Solve corners 
Step 1: Solve Centers

For each face, there are 4 center pieces. Start by getting the 4 white center pieces together on any face. This is normally extremely simple.

Next, get the opposite centers done, in this case yellow. A standard move shown in the video below is to put a new piece into position without disturbing the existing pieces. To do this, we push out the piece we want to keep with the new piece, then turn the face and finally return the piece we pushed out.

Once two opposite centers are done, it's time to choose any of the 4 remaining center colours. I'll choose blue.

Caution: Even though you can put the blue centers on any of the remaining faces, you must make sure that the next center you choose actually belongs there. Find the corner with white and blue on it. It should also have a red sticker. Hold the cube so that the white corner is on top. The red centers must be placed to match the corner. So if your corner piece has white on top, red left and blue right, then your centers need to match.

The remaining three centers are placed in the same way as above.



Step 2: Pair Edge Pieces

All centers are now in place and it's time to pair edge pieces. You'll notice that instead of there being 1 edge piece joining two faces, there are two. The goal is to match 9 edge pairs, and then use the edge piece series on the last 3 to complete all 12. Use the edge piece series as follows
  1. Find two edge pieces needing to be paired.
  2. Bring them together (centers will be disturbed).
  3. Use an edge piece series to move the paired edges onto a different face. Make sure that piece 3 is not already a matched edge pair. And if possible, use the 3rd piece so that it creates a 2nd completed edge pair.
  4. Return the centers.
Help! I Only Have Two Edge Pairs Left To Make?!?

If you happen to accidentally pair 10 edge pairs, leaving only two remaining, there's a simple fix. There's no easy way to explain it though, so straight to the video!



Step 3: Place Edge Pairs

Now treat each edge pair as a single edge piece. Position the edges exactly as you would for the 3x3x3 Rubik's cube.

If you find yourself with the last two edges needing to swap, just turn the upper face one turn, and then re-solve edges using an even number of turns.

Help! My Last Edge Pair Is Flipped?!?

On this cube, it's perfectly possible for all edges to be placed, but the final edge to be flipped in its position. Here's what to do:
  1. Turn the two bottom slices 1 turn
  2. Re-solve each face's centers in order,using the same "push-out" technique as previously
  3. When all centers are re-solved, 3 edges will be unmatched
  4. Re-pair these remaining edge pairs, then re-place the edges
It's easy when you see it in action, and this video will take you through all aspects of placing edges.




Step 4: Solve Corners

This is the same as for the 3x3x3 Rubik's cube. Carry out corner piece series

U R U' L'  U R' U' L     (and mirror)

until you have only 3 corners remaining. Then to place the final three corners, we have a couple of options. One option is to again use the corner piece series, which often involves some setup moves. The other option is to place the pieces into position without worrying about their orientation. Then, orient each corner using an adaptation of the edge piece series.

(FR'F'R) x 2   L  (R'FRF') x 2   L'

This will twist the UFL corner anticlockwise and the UBL corner clockwise.

Help! Two corners Need Swapping?!?

On the 4x4x4 cube, it's perfectly possible to end up with the final two corners needing to be swapped. It's not possible for this to happen on the 3x3x3, and so this is one of the differences with this puzzle. The case where two corners need swapping and a 3rd is in position but twisted is the equivalent case.

The problem we have is that we have one set of swapped corners but no sets of swapped edges. We need to create a set of swapped edges. My way of doing this is as follows.
  1. Rotate the bottom half of the cube 180°
  2. Remove the unmatched edge pair using an edge piece series, then replace it flipped.
  3. Turn the whole cube around 180°
  4. Remove the unmatched edge pair of the same colours as before using an edge piece series, then return it flipped.
  5. Rotate the bottom half of the cube 180°
In algorithm form, this is

(Dd)2  F'UFU'  RU'R'U  y2  F'UFU'  RU'R'U  (Dd)2

At this stage, your cube has two swapped edges to go with the two swapped corners. Proceed as normal to re-position the edge pairs and solve the corners.

Again, this is much easier to understand by watching it happen.




And that's it. Your 4x4x4 Cube is now solved. I trust this site has been helpful. If you have any questions or want some clarifications, please use the comments to do so. 


13 comments:

  1. Hi. I have a question.

    In the video demonstrating the end game, you make piece 1 the corner that goes across the cube diagonally. However, on the page for the end game, it states this. "Find any corner piece which will roll over along a cube edge into position. Call this piece 1."

    Can piece 1 for the end game be ANY corner, including the one that goes across the cube diagonally?

    Thanks.

    ReplyDelete
    Replies
    1. Hi Timothy

      Yes! Piece 1 can be any piece. In the original explanation, I think Marshall tries to keep it simple by sticking with "a piece that will roll over along a cube edge". But sometimes you don't have any pieces which will do this. He then says "turn a face to create a piece that will roll over along a cube edge". That's one method.

      The other method, often just as simple, is to start by making your "cross the diagonal" piece 1, and go from there. You should always look for the most convenient method to use. If there is a piece that will roll along an edge, I'll use it for sure. (But you'll notice I didn't have that in the video end game.) But when there's not one of those, I'll just use a diagonal piece as piece 1.

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  2. Can you please add subtitles to the videos?

    ReplyDelete
    Replies
    1. Hi

      Sorry, no. This site takes a long long time to keep going and to make the videos. I also have a normal day-job. I simply can't put any more time than I already do into the site.

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    2. hey twistypuzzling, I love the videos, I love the tutorials, and I understand you're busy, but what if you found a second person to help you maintain the blog (or something) to lighten your load. just a thought :P

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    3. Sam, are you volunteering?! (serious question)

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  3. Hi again,

    When i have 2 corners need swap (with no 3rd miss-oriented), is it ok to the same procedure ?

    ReplyDelete
    Replies
    1. It's on this same page, under Corners, with the heading "Help! Two corners Need Swapping with the 3rd Corner Misoriented?!?"

      Delete
    2. Sorry, i meant, only 2 corners need swap (no problem with 3rd corner), should i "make" the third corner miss-oriented ?

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  4. I have a method of solving, first I do the top and bottom centers, then the corners, then all the top and bottom edges, then the remaining edges, then finally the rest of the four centers, for me myself seems easier for me because I don't have to try to match as many edge pieces together

    ReplyDelete
  5. Hi there! Love your site & refer to it often. This is the first page that I've encountered where there don't seem to be any videos ... (And I'm a bit stuck on those last two edge pairs!). Any chance you could post a direct link to your YouTube video for edge pairs?

    ReplyDelete
    Replies
    1. Thanks. It's definitely a browser issue. I just loaded this page in both firefox and chrome. Firefox, works perfectly, all videos are there and play. Chrome: no videos show up at all. I even tried opera and the videos work perfectly there as well. Chrome's the problem.

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    2. Thanks for your quick reply. I'm using an iPad and except for this page, all videos that I've viewed here have worked perfectly... Curious... Well, if I can't get unstuck, I'll just visit on my computer. Very much appreciate your attention!

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