## Friday, August 21, 2015

### 2x3x4 Camouflage Cuboid Reduced to 2x2x4

After working out a solution heavily relying on commutators and having one part that was totally baffling and that although I always found a way through I never really fully understood—anyway it dawned on me that the puzzle could be partially scrambled as a 2x2x4 and that made the solution much easier. So, although I am not real keen on reduction methods for most puzzles I thought that reducing the scrambled 2x3x4 to a 2x2x4 would make it much easier to solve. After a few such solves I was feeling confident enough and curious enough to watch Twisty Puzzling's tutorial. He reduces all the way to a 2x2x2. I suspected that would be his approach. :)

In trying to refine my method of reducing to the 2x2x4 I have run into a situation that is almost as bothersome as my first method was. Let me show you.
In pic 1 you see the scrambled state for this solve. My strategy in reducing to a 2x2x4 is to attach yellow and white edges to the 4 orange corners. The red corners stand alone due to the axis of rotation that is between the red and orange layers. The other skinny edges make up the middle layers of the reduced 2x2x4. Look at pic 7 to help visualize this if necessary.

Pic 2 shows the Orange Green White block reduced.

Pic 3 shows the Blue Yellow edges in place to slide over the Orange Blue Yellow corner, but the Blue Red edge is blocking it. It was a real struggle for me to get past this without losing track, but on a subsequent solve I think I figured out an easier way to deal with the situation. Namely, twist the corner made of the corner plus two edges so the Blue Red is horizontal. Then replace the Blue Red with an edge-center pair. Then twist it back so the Blue Yellow is back in place ready to slide over the Orange corner.

Twisting Corner Blocks. Using 2x2x2 moves do things like ( R U Ri Ui ) x 2 or ( R Ui Ri U ) x 2 or the left-handed versions, to orient corner blocks. Only one corner on the bottom layer gets twisted, so the bottom is the working layer where pieces are paired up. Three pieces in the top layer get twisted, but since they are corner blocks, already reduced corners do not get unreduced.

Pics 4 and 5 show two more reduced Orange corners. Somewhere during the hassle of getting the Orange Blue Yellow the 4th Orange corner got reduced too.

Pic 6—once the Orange corners are reduced it is ready to solve as a 2x2x4 Tower. For me that means solve the corners ignoring the middle layer edges and centers. Oh wait, I don't totally reduce it to a 2x2x4 since I ignore the centers until the end.

Pic 7—To solve the middle layer edges of a 2x2x4 I use the same technique as when solving the corners of a 3x3x2. With the 2x2x4 do not twist the top or bottom layers or they will get scrambled as the middle layers get solved. Just move the middle layers and the orange, red, blue, and green layers. When I say the orange layer I mean the reduced layer. Any color can be on the front when using the 3x3x2 corner cycling commutator. I use things like ( u L2 ui R2 ) x 2.

Pic 8—The final step is to solve the centers. With Red on the right the following moves the square center on the Bottom Back to the Bottom Front and the Bottom Front to the Top Back.

( M2 U M2 Ui M2 ) Di ( M2 U M2 Ui M2 ) D

Sometimes this isn't what you need. If you need to cycle from Bottom Front to Bottom Back to Top Back, still make sure Red is on the right and do the following.

Di ( M2 U M2 Ui M2 ) D ( M2 U M2 Ui M2 )

Now that I have used the reduction to 2x2x4 method a couple times and am feeling comfortable with it I wonder if I could apply the corner twisting strategy to my first method in the step that gave me so much trouble to make it very easy to solve without any reduction. There is something about starting with the corners and filling in all the edges from there that really appeals to me.

(9/3/15) I pretty much like the reduce to 2x2x4 method. Another thing that is helpful at times is ( RU RiUi ) x 3 to invert a column. Also 3-cycles when they aren't blocked help out sometimes.