Message #3915

From: Melinda Green <>
Subject: Physical 2x2x2x2 - Canonical moves
Date: Thu, 04 Jan 2018 15:28:32 -0800

First off, please check out Zander Bolgar’s lovely solution video <> that he invited me to share. It’s very cool to see someone developing something like finger tricks and blasting through a solution. It’s very much like Bob’s <> and Joel’s <> solutions as well as Marc’s <> approach.

This makes for a great launching point for questions about which moves should be included in a canonical set. Of course any move that results in a reachable state can be justified in a solution, but there’s such a spectrum from "obviously fine" to "obviously not". Now that we’ve gotten some experience with this puzzle and the practicalities of solving it, I feel it’s time to see if we can find some sort of natural canonical set, so I’d love to hear your thoughts.

Here is the list of moves I know about, loosely ordered as described above:

  1. Simple rotations
  2. 90 degree twists of outer face
  3. 180 degree twists of side face
  4. Center face axial twist
  5. Arbitrary half-puzzle juxtapositions
  6. Clamshell move
  7. Whole-puzzle reorientations
  8. 90 degree twist of side face (each 2x2x1 square rotate in opposite directions)
  9. Single end cap twist (with parity restrictions?) [fine for scrambling]
  10. Restacking moves [fine for scrambling]
  11. Single piece flip
  12. Reassemble entire puzzle

I suspect the trickiest part has to do with #9 which is the one I would most like to nail down.

I intend to create a follow-up video to talk about all of these and any others you can think of. The way you can help is to offer additions and corrections to the above list, and especially in suggesting ways to reorder it. Then please suggest where you’d draw three lines:

* Everything above is primitive (Or "basic" or "elementary" as Joel calls them)
* Everything above is canonical. IE always acceptable in solutions
* Nothing below is acceptable in solutions.

Thanks all!