Message #3924

From: Marc Ringuette <>
Subject: Re: [MC4D] Physical 2x2x2x2 - Canonical moves
Date: Fri, 05 Jan 2018 10:51:07 -0800

I think that in a year, there will be 2 or 3 rule sets in common use.  
This is a good thing.

As Roice says, it’s pretty clear that for a good 2^4 hypercube
correspondence, all twists should alter 8 piece positions at a time.  
We may end up with multiple rule sets that obey this constraint (and,
for instance, allow or disallow various physical macros and/or virtual
macros for moves that do not have a 1-1 correspondence; if you recall,
the whole puzzle cannot be solved without at least one such move).   
Bob and Joel both used versions of this approach, and will perhaps
provide us with more detail about what they did.

It’s also pretty clear that another nice way to use the puzzle involves
allowing 4-cycles.   Both I (a few months ago) and Zander (in his video
just now) gravitated naturally to solve the puzzle that way.   It makes
the puzzle easier, but not absurdly easy, and still lets us encounter
fun 4D challenges.   It’s also less likely that you will accidentally
find yourself in an illegal parity state:  permutation parity does not
exist, and as long as you don’t drop the puzzle in such a way that
single pieces are ejected, orientation parity will not be violated
either.   This bypasses one modest "pain point" of the other rule sets,
where you discover toward the end of a solve that you have been in an
illegal permutation parity state all along, due either to sloppy
scrambling or a slip of the hand during the solve.

So, let’s remember not to think of "legal move" as a single binary
distinction that will apply to all users of the puzzle.   Let’s define,
and name, multiple rule sets and see what we like!