I got a Rubik’s 4x4 in the mail on August 29 compliments of Discover Rewards. "It pays to Discover."

At first I just tried a couple familiar 3x3 algorithms on it only turning the outer edges. I decided if I only turned the outer edges, it behaved just like a 3x and could be solved just like a 3x. After awhile though I had to turn the middle. Let's let R mean what it does with the 3x3, that is, a turn of the Right face clockwise. Say r stands for the layer that is in from R. L is still left, but l is the layer that is in one from L. An li then would be a turn of the layer just inside the Left face counterclockwise.

I did R li and made stripes around 4 of the sides. Then I turned the whole cube and did it again. And again and again. Many many times. It made some interesting patterns. Stripes, fishies, checker-boards, and even got back to a solid color on one side at a time, although the edges were not all in the right places. 

Finally I just scrambled the whole cube until it was nice and mixed up. With the 3x3 I did not even attempt to solve it on my own without help. Well, I guess back in the 80s I did, until I found a couple books explaining how to do it. Then I put together a method of solution I liked from the stuff I’d read and learned it. Eventually I quit playing with it and forgot how to solve it. When I got interested again this year I looked for solutions online immediately that I could learn. It has been fun learning not one, but several different ways to solve the 3x3. LBL (Layer By Layer) with and without a working corner, F2L (First 2 Layers) corner/edge pairs, Petrus, Corners First, and the Ultimate Solution.

With the 4x4, I didn’t want to look up a solu-tion online before I spent some time trying to figure it out on my own. My first observation was that the sides are not defined by im-movable centers as they are on the 3x3. With the 4x4 there are 4 centerish pieces, but they can all separate and move around the cube just like the edges and corners. So my initial attempt was to start with the 4 center squares on each side. I got the whites pretty easily. Then opposite the whites I did the yellows. It was not quite as trivial since you have to think about the whites as you get the yellows. But it wasn’t hard. Then I got the greens. It wasn’t so bad, but then getting the blues opposite the greens took a little more thought. I think I could do it again. After getting those four sides that just left the red and orange sides. As it turned out I got the centers, but when I tried to get a solid layer some of the center pieces got misplaced. I ignored them and tried to proceed getting 2 full adjacent lay-ers. I got within 1 edge piece. But then things just started getting worse. So I scrambled it up and started over. I decided to try starting with a 2x2x4 column. After at-tempting that for awhile I decided to instead go for a 3x3x3 block.

Next, I decided to go for a 3x3x4 block and it didn’t take too long to get it. The thing is, I didn’t know if I was lucky on any of these steps, or if I was using a sound strategy for

solving it that will be just as easy every time. When I had 3 corners and 9 edge pieces to go I had a feeling I wouldn’t get much farther. I hadn’t used any algorithms. I’d gotten this far by just moving pieces around 1 or 2 at a time. No help. No hints. But I was stuck. I used the 3x3 corner swap and orient sequences to get the remaining 3 corners. That left me just 9 edges away from getting it. After using another 3x3 edge cycle algorithm I knew I got 1 more edge. Just 8 edges away from solving it. I somehow got within 7, but then gave up and messed it up to try a new strategy.

My first strategy of August 30 was to go for all the edgepairs first. I knew I could then get the corners using 3 cycles and if neces-sary twisting a pair in opposite directions. I figured I would ignore the centers so as not to have to think of too many things at once. Well, it worked... mostly. I guess if it only mostly worked, it didn’t work. I ended up with one edgepair that needed to be flipped and two corners that needed to be swapped. I didn’t know an easy solution for that. And, of course, the centers I ignored fell where they may, which was not into place.

My next idea was to start with one edgepair and make a stripe all the way around the cube, then get the two remaining centers and go from there. I thought I was making progress, but kept scrambling one thing to get another. So I tried something else. I tried to solve the red, white, and blue sides so I would have what looked like a 3x3x3 on the other side. This strategy also ended close, but not solved. I was just about ready to start looking for solutions online, but fortunately our internet service was down.

Before the day was over I decided to start with a 2x2x4 column, then expand it to 3x3x4, then 3x4x4, then see what the Last Layer looked like. I don’t recall how far I got, but I didn’t take any pho-tos past the 2x2x4 if that is any indication.

On August 31 I got internet access back and took a look at bits and pieces of websites, but I still didn’t want to just learn someone else’s solution. I wanted to get as far as I could on my own, and didn’t feel that I had reached the limit yet. I read some introductory remarks here and there. One suggestion was to first solve all the centers, then get all the edges together with their twins, then solve it like a 3x3x3. I tried. I got all the cen-ters and was getting more comfortable with the strategies I’d worked our for getting them. Then I worked out a system for joining edge pairs, but once I got 8 pairs I was stuck. My method left 4 edgepairs un-matched. So I just went on to getting the edgepairs into place, then fixing the corners. I was left with only 5 edge pieces out of place.

September 1 on the way to Jim and Ro-sanna Rutherford’s wedding I got within 2 pieces of solving it. I still hadn’t looked at any solutions online. I got the centers, then as many edgepairs as I could, then moved the edgepairs into place as well as possible,

then moved the corners into place and oriented them when needed. The big challenge was getting the centers and edgepairs.

On the way home I got it down to 2 pieces again.

September 2 I rediscovered a website that I thought would help me understand better some of the practical theory behind some of the algorithms that I had been using in solving the 3x3. I was hoping that understanding the math, the group theory, and how it relates to the 3x3 would enable me to dis-cover on my own the sequences needed to finish solving the 4x4. http://grrroux.free.fr/begin/Begin.html

Later on September 2 I wrote: “Break-through! I finally figured out how to match all the edge pairs up. I think. I’ve only done it this once, so I’ll only know for sure if I can do it consistently. But since I only have one 4x4 and am not finished with the attempted solution I am explaining on this page, that little issue will have to wait. After matching up all the edge pairs I just moved them around the cube into their proper places. Some I just used simple twists and turns, then I used The Ultimate Solution Edge Se-ries (4 twists) to get the rest. After that it was just a matter of putting all the corners in the right places and orienting them correctly. I thought I was home free. I was using The Ultimate Solution Corner Series (8 twists) to fix the corners, and sometimes the twist two corners sequence from the Working Corner Solution that I know. A weird thing hap-pened. I got down to two corners needing to be swapped. I know a sequence for swap-ping two corners (part of the LBL method I learned for the 3x3 at Jasmine’s site), but I knew it would mix up some edges. Not hav-ing much choice, I went for it hoping I would then be able to solve the edges. After get-ting the corners in the right places and ori-enting them correctly, I had another strange situation. Two edgepairs needed to be swapped. Like the 2-corner swap, this is an impossible situation on a 3x3. I figured I’d play around with The Ultimate Solution Edge Series and see what I got. I ended up with an edge situation that can be fixed with URURURURU. That’s what we call it, anyway. For those of you familiar with the notation, it isn’t all clockwise! This is also part of the Working Corner Solution I learned from Mark Jeay’s site. After using URURURURU I had five corners to fix. Doing all the edge sequences moved some corners around. After doing what I can do with the corners—Argh! Two need to be swapped! I need to figure out how to swap 2 cor-ners without affecting the appearance of the rest of the cube.”

Still on September 2 I finally got it. But I still hadn’t figured out how to deal with the situation when I needed to swap two corners. I just figured I’d try it again to see if I could get all the edgepairs again. It took me awhile but I figured it out. It was really fun figuring things out without just following an on-

line guide. So how long did it take me to solve the 4x4? 4 days.

It was time to get help. No, not that kind of help. Oh wait, back to the cube story. I found two places online that had helpful information about dealing with the swapped corners and flipped edges that show up at the end. One was by Chris Hardwick, and one by Philip Marshall. I liked parts of both, so incorporated the parts I liked into my personal solution.

On September 4 I recalled reading some-where that getting the centers last would avoid the problems with corners and edges at the end. So I tried it. I did not succeed. I ended up with swapped corners and a flipped edge anyway. Perhaps it was because of the way I tried to get the centers. I still hadn’t read anyone’s complete solution yet. It dawned on me I should try the Edge Piece Series only with r and f instead of R and F and see what happened. It did two 3-cycles of center pieces. So I solved all the edges and corners then attempted to use my new-found center piece cycler to finish up. I got close, but couldn’t figure out how to finish it up.

By September 13 I had two pages of notes for solving the 4x4. One is based on getting the centers first, then all the edgepairs, then solving it as a 3x3, doing the fixes at the end if necessary. The next is based on Dave Baum’s solution, but has some adaptations to include more things I already knew how to do using Adam Cheyer’s Corners First method. One nice thing about this method is that you get the corners early and get the centers last, and this somehow avoids the parity problems of the other method. Another nice thing about it is that his Edge 3-cycle is so very much like the way I had figured out to match edgepairs, that it was easy to remember. Another nice thing is that the se-quences of moves that move center pieces at the end make a lot of sense, and so are easy to re-member.

October 2 version:

A Centers Last Solution based on the one by Dave BaumThis approach avoids the parity problems by leaving some inner slice operations until near the end.

1. Solve the white and yellow centers.2. Solve the white and yellow corners. I use the Corners First Method for solving the 3x3 from Adam Cheyer.3. Fill in the white & yellow edges. Make some edge pairs if you want. Use the Corners First 3x3 method as

far as it works. Alternately you can use the Revenge Edge 3-Cycle (or its mirror and/or inverse). Or per-haps a combination. If you need to make edges cross over from the l to r layers, do F2 R2 L2 B2 R2 L2.

4. Place the l layer edges next to their L layer corners with F2 –r F2 r2 F2 r F2 (swaps UFl & UFr).5. Solve the edges in the r layer. Sometimes it is possible to turn the r layer such that one edge is correct

and the other three can be placed using the Revenge Edge 3-Cycle (using conjugation). If two diagonal pieces are in place use the 3-Cycle to move them and a third piece. Now move the r layer so one is in place and use the 3-Cycle to position the others correctly. You want to hold the cube such that two pieces to be cycled are in front and the third is on the top in the back. Turn the back so the piece is on a side layer and spin that layer 180˚ to bring the piece to the front so it can be cycled. After the cycle, undo these setup moves.

6. Fix the centers. You usually have to turn U or L or R so the ones you want to swap are lined up correctly. Set it up, then after the swap, undo the setup move.

L U To swap these pairs do the following Front View moves:2 2

L U To swap these pieces do the following Front View moves:22

L R To swap these pieces do the following Front View moves::22

D U These pairs are both in the f layer.To swap these pairs do the following Top View moves:

2 22

2Top View

The Revenge Edge 3-Cycle

r (–U R U) –r (–U –R U). This moves DrF to UrF to uRF to DrF.

–l (U –L –U) l (U L –U). This moves DlF to UlF to uLF to DlF.

–U R U r –U –R U –r cycles backwards which should be a handy thing to do, although I’ve never bothered.

based on Adam Cheyer—Corners First http://www.ai.sri.com/~cheyer/rubiks/rubiks.html

Step 1. White X Down

Step 2. Yellow X UpNo yellows up / out the back: R2 U2 R U2 R2 No yellows up / out the side: R U R2 –F R2 U –R (Ortega)(hold two yellows out the front face)

(the only two you absolutely need)1 yellow up / clock: R U –R U R U2 –R (Sune) (yellow FL)1 yellow up / counter: –R –U R –U –R U2 R (Sune) (yellow BL)

2 yellows up / out the back: R U2 R U2 R U R2(hold up-yellows at Front)

2 yellows up / out the side: R U –R –U –F –U F(hold up-yellows at Front)

2 yellows up / diagonal: (–F U F U) (R –U –R)(No yellow on F face)

Step 3. All X’s (if you do a 1, White may end up on top)No pairs: R2 F2 R2 (doesn’t matter)1 pair: R2 –U R2 U R2 –U R2 U R2 (pair on bottom left)

2 pair: R2 U R2 U2 F2 U F2 (pairs on front)4 pair: 2 twice5 pair: 0 then 1

Step 4. 3 U-layer edges (either W or Y; really could be any!)You can hold it however it feels best and smoothest and make modifications to the twists to suit your style. Also sometimes you need to go the other way, or just simply want to.

M D2 –M (t-color on D face in Front)R E –R (t-color on R face in down layer)F –UD –R (t-color on B face in middle layer)

Step 5. 4 D-layer edges (the Keyhole is the U-layer edge that was not filled in)d-color in middle layer facing back; Keyhole in front; twist bottom of front toward d-color cube and insert the edge be-tween the corners. When I twist and turn this correctly is flows very smoothly. Hold the cube with the left hand with your thumb on UL and ULB, and your index finger on UR and URB. Sometimes you have to get a bad d-color in the D layer up to the M layer by twisting the front and spinning it to the back. Sometimes it works to put the last d-color backwards into the keyhole, then fill the keyhole with its piece. This accomplishes step 6.

Step 6. Last edge on layer 1Move the top so both the keyhole and the last edge in the middle layer that needs to fill the keyhole (the Key) are at the front of the cube, with the u-color facing to one of the sides. Using one of the 4 sequences below, move a d-layer piece to the keyhole and then insert the key into the keyhole, putting the d-layer piece back where it belongs.

FL to UF preserving BR: F d–D –F –UD –R d–D RFL to UF preserving FR: –F –dD F –UD –R d–D RFR to UF preserving FL: F d–D –F U–D L –dD –LFR to UF preserving BL: –F –dD F U–D L –dD –L

Key on left Keeper on BR start clock—Key upKey on left Keeper on FR start counter—Keeper upKey on right Keeper on FL start clock—Keeper upKey on right Keeper on BL start counter—Key up

Step 7. Move final edges3 cycle: M U2 –M U2 (start with correct one at FD)= pattern: (M2 U2 M2 U2) to swap front top w/ back top AND front bottom w/ back bottomX pattern: F2 (=) F2 to swap front top w/ back bottom AND front bottom w/ back top

Step 8. Flip final edges (–M –U)2 –Md2 (–M –U)2 U2 (flips UF and UB) Sometimes you must do a B2 or U2 to get them both on the U-layer. Or just don’t do U2 in step 7 if you see it coming. Then undo after the flip. Sometimes you have to do the flip twice because you have 4 edges to flip.