Message #4112

From: Marc Ringuette <>
Subject: Re: [MC4D] 2x2x2x2: mini-puzzle "twisty stacky 2^3"
Date: Sun, 02 Sep 2018 10:42:55 -0700

Hi, Melinda, thanks for the thumbs-up.

So far, the name of the mini-puzzle is just its description, the "twisty
stacky 2^3".

I’ve already solved it in a straightforward way; I’d say its difficulty
is 1/10 or 2/10 if you already know how to solve the regular twisty 2^3,
compared to about 8/10 for the full 2x2x2x2 puzzle.   So, I think it’s a
really nice stepping stone that eases you into reasoning about the 12
orientations of the pieces, and how to "get access to" different corners
by moving them on and off the outside.   It seems particularly nice for
someone who has become stuck in trying to solve the full puzzle.

I’m not sure about the relation to other 4D puzzles.  I’m tempted to
guess that it’s a physical 3D version of a 4D 2x2x2x1 twisty puzzle, or
something like that.   That’ll be fun to think about later.

Spoiler alert!   If you’d like to enjoy figuring out the twisty stacky
2^3 totally on your own, you should probably stop reading and go do
that.   In fact, I should have put a spoiler alert on the link to my
monoflip video.   The initial intro video, however, is spoiler free.

(hint #1) – One horribly inefficient way to solve the puzzle is to just
"monoflip" each of the purple corners to the outside, one by one, using
the algorithm I gave in my 2nd video, and then use any 2^3 method on the
result.   There are no weird cases; you just reduce the orientations to
the ones of the twisty 2^3 and then solve.   I think it would be much
more satisfying, though, to find your own way of putting "purple corners
out" in groups of four.

(hint #2) – If you take the solved puzzle and apply the moves E R E,
you can see that the corners that were pointed into the center of the R
face have moved to the outside, and vice versa.  The left half of the
puzzle is unchanged.  Then applying E R’ E will go back to solved.

(hint #3)  Once you’re down to one or two non-purple corners, think
about conjugating E R E with a corner twister algorithm.   This is more
or less what I did with my monoflip.


On 9/1/2018 10:53 PM, Melinda Green [4D_Cubing]
> How clever you are, Marc! That’s a neat little puzzle. Some questions
> immediately come to mind:
> * Is "twisty stacky 2^3" the name or the description?
> * Have you solved it?
> * Does it have any relation to the 2^4 or any other puzzles? Your
> monoflip seems to hint at such a thing.
> * How does the difficulty compare to both the 2^3 and the 2^4?
> * Exactly how useful is it as a stepping stone to the full puzzle? I
> love how the puzzle currently doubles as a simple take-apart
> puzzle for young children, and is probably where even active
> cubers should start simply to get more familiar with the topology.
> Your puzzle may fit very nicely in difficulty between take-apart
> and full puzzle.
> * When solving this puzzle, can it be easily reduced to a pure 2^3,
> or are the restacking moves more integral? And does that even matter?
> The last question will probably take some time to answer, but perhaps
> you or other list members will be able to inform the other questions.
> What a nice little bonus puzzle!
> -Melinda
> On 9/1/2018 11:21 AM, Marc Ringuette
> [4D_Cubing] wrote:
>> Hi, 4D puzzlers!
>> If you already have Melinda’s 2x2x2x2, then you can easily try this fun
>> mini-puzzle.
>> Take half of your 2x2x2x2 puzzle (I put the pink-purple corners out, set
>> aside the pink half, and use the purple half).   This is the solved state.
>> The puzzle is called the "twisty stacky 2^3", and the rules are as
>> follows.   The puzzle can be face-twisted like a 2^3 Rubik, plus you can
>> make any of the three restacking moves E, M, and S.   Scramble and solve!
>> Here are two YouTube videos – a brief intro, and then a demo of my
>> monoflip (yes, it has one!) for the puzzle.
>>      30  Intro to twisty stacky 2^3    1m33s
>>      31  Monoflip for twisty stacky 2^3    1m52s
>> This cute little puzzle is a lot easier than the full 2x2x2x2, and yet
>> its pieces still share the 12 possible orientations of the pieces of the
>> full puzzle.  I find it to be a useful training exercise for the larger
>> puzzle, as well as being fun to play with.
>> Enjoy!
>> Marc
>> ————————————
>> Posted by: Marc Ringuette<>
>> ————————————
>> ————————————
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