Message #865

From: Melinda Green <>
Subject: Re: [MC4D] Fractal cubes
Date: Thu, 11 Mar 2010 18:43:12 -0800


Indeed I failed. I do that a lot. ;-)

I didn’t have a proof of my guess, but that’s what my "I think"
equivocation meant: It was just my guess. It seems entirely clear to me
that inner stickers cannot mix with outer stickers given the twists
we’ve talked about so far. I’ll go even further and say that I’m pretty
sure that inner stickers can never be adjacent to any outer stickers
that are not on its own cubie. As to a proof? Well, let’s see. Level-1
cubies with inner stickers will always have two inner and two outer
stickers arranged in a ring: outer, outer, inner, inner. Given a uniform
pristine coloring like we’ve been considering, every level-1 edge cubie
with outer colors O1,O2 will have inner colors I1,I2 that are identical
to every other cubie with the same pair of outer colors. Since all edge
cubies with the same pair of outer stickers are identical and there is
only one correct orientation for any edge piece, it seems to follow that
once all of the outer stickers are placed correctly, all inner stickers
will also have to also be correct.


David Vanderschel wrote:
> Melinda, relative to my previous post in this thread (which was
> primarily a response to your preceding post), you failed to
> answer a direct question for which I was eager to see your
> answer. So I will repeat the question.
> You had written:
>>> Regarding the coloring of inside stickers, I didn’t
>>> completely follow what you [Chris] proposed, but it
>>> doesn’t seem like an important issue because I don’t think
>>> that the inside stickers can contribute to the puzzle. I
>>> think they should automatically be correct when the rest
>>> of the puzzle is complete.
> and I had asked:
>> This is not obvious to me. Do you have proof, reasoning,
>> reference? I thought this was the interesting thing about
>> the order-9 variation.
> Regards,
> David V.