Message #4079

From: Jay Berkenbilt <ejb@ql.org>
Subject: 2x2x2x2 solution and analysis
Date: Sun, 29 Jul 2018 21:25:01 -0400

Hello all – this is Jay Berkenbilt, one of the longest time members of
this group, and the second ever solver of mc4d back in October, 1998. I’ve
been mostly lurking on this list since its formation, popping up every now
and then. Several weeks ago, I ordered my physical 2x2x2x2 puzzle and then
sequestered myself to do my own analysis and solution, free of spoilers
from the list. I have completed this, and I’m now ready to share my work,
dive in, and join all the discussions. I’m looking forward to contributing
and learning.

I have created a YouTube channel
<https://www.youtube.com/channel/UCedJ9DbblmqBq4H_gWzdL6g/videos?flow=grid&view=0&sort=da>
with
my solution videos. You should view these "oldest first". The videos are
numbered in order and also linked below in order. Clicking "Play All" will
show you my videos in reverse order. I don’t know how to fix that.

My solution method is as follows:

• Do a full scramble
  
• Get all the blue and green stickers off the corners – some will be on
  and some off right after full scramble, and the next stage works better if
  they are all off the corners
  
• Get all the blue and green stickers onto the corners starting from all
  of them off the corners
  
• Solve the blue slice
  
• Solve the green face as much as possible; sometimes there will be a
  single corner out of orientation or a pair out of orientation such that one
  can’t be rotated using regular 3D Rubik’s cube moves
  
• Resolve the final corner orientations

It typically takes me about 15 minutes to do a full solve. I tend to do
things in a fixed order rather than doing much exploitation of things that
coincidentally happen to be in an ordered state.

I have created a series of 11 videos, each ranging in length from about
2:30 to just under 10 minutes, but most are in the 4 to 8 minute range. The
videos are as follows:

• 00: 0:39 personal introduction <https://youtu.be/h8vtOh58PQE>. You can
  skip this unless you’re curious about who I am and what I look like. :-)
  
• 01: 5:18 mapping to mc4d <https://youtu.be/0WcvKsUisqs>. This is my
  discussion of how I map this puzzle to the software mc4d puzzle and how I
  label the slices.
  
• 02: 9:19 gyro <https://youtu.be/50Cjqwy2oj8>. My "gyroscopic rotation"
  video. Here I present my algorithm for the 4D rotation that moves some
  other slices into the top and bottom positions. I describe in detail how to
  look at this and how and why it works. My sequence is different from the
  one in Melinda’s introductory video and requires only five moves with no
  "cleanup" moves.
  
• 03: 4:06 scramble <https://youtu.be/xJ7YEeE0yTs>. This is the full
  scramble I used for the solution. I’m using a previously posted method for
  scrambling, but I describe from first principles why it is valid.
  
• 04: 7:59 blue green off corners <https://youtu.be/_b3GWpD6_VA>. First
  solution stage: moving all blue and green stickers off the corners. I also
  introduce a few move patterns I use systematically throughout my solution.
  
• 05: 6:14 blue green to corners <https://youtu.be/Be8qJ3AbF_A>. Second
  solution stage: move all blue and green stickers back to the corners. It
  turns out in this case to be all but one, which happens sometimes.
  
• 06: 5:02 solve blue <https://youtu.be/IMNfgkTBIto>. Solve the blue
  face starting from all the blue stickers on the outer corners.
  
• 07: 3:53 green except last corners <https://youtu.be/1ru-3RV022Q>.
  Solve green down to one pair of corners out of orientation such that one of
  them can’t be fixed using regular 3D Rubik’s cube operations.
  
• 08: 4:08 final solve <https://youtu.be/dTfL_UjMIxc>. The final
  solution, resolving the pair of non-oriented corners (or "disoriented", as
  I say in the video), with a clear explanation of how my method works.
  
• 09: 6:00 corner monoflip demo <https://youtu.be/eu14WmUzmnI>. A
  stand-alone video showing my algorithm for fixing the single corner
  monoflip issue. My algorithm is 34 twists, counting twists of a half slice
  (treating one face as a 3D Rubik’s cube) as a single twist and counting the
  gyro as zero. (One could argue that the half twist should count as two
  because how it is justified, but I’m counting it as one here.)
  
• 10: 2:30 pair swap demo <https://youtu.be/zscALET96LY>. A stand-alone
  video showing a common sequence I use to swap two pairs of corners. I use
  this various times during the solution (contrary to what I say in the
  video), but this video demonstrates it in an otherwise pristine puzzle,
  making it easier to follow and understand.

Each video has a descrption with slightly more detail. I hope you enjoy
these. I’m looking forward to feedback and commentary.

–Jay