Message #1051

From: Andrey <andreyastrelin@yahoo.com>
Subject: [MC4D] Re: definition of a twist
Date: Tue, 20 Jul 2010 18:50:59 -0000

Melinda,
Situation with the sequence of twists of the same side with different masks is a little more difficult. It looks like we should check the rotation of each layer after this sequence, count the number C of different rotations and say that actial number of twists is C-1. E.g. if we rotate two opposite sides of 3^3 clockwise, it counts as two moves in any metrics that I know (save for 3-colored nonoriented 3^3 - in that puzzle it’s one - and only possible - twist :) ).

Andrey

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:
>
> Matthew,
>
> I know it’s been discussed too but I’ll just give my current opinion
> which is that I like the idea of defining a twist as any combination of
> currently supported twists on a single face that can be reduced to a
> single one with a single slice mask. So a twist with one slice mask
> followed by the same twist with a different mask should only count as a
> single twist and represented in the log file with their combined mask.
> Likewise three 90 degree twists should only count as one -90 degree
> twist. And of course any combination that leaves the puzzle unchanged
> shouldn’t count at all. I currently cancel pairs of twists that are the
> inverse of each other, so long as they don’t cross macro boundaries. I’d
> love to support more such cases.
>
> The one case that I’m not currently ready to accept are combinations of
> face twists that can be represented by a single transformation but which
> are not reachable by a single existing twist. I’m talking about moves
> like double 90 degree twists. At first blush that seems reasonable to
> represent as an atomic move but look at the Onehundredagonal Duoprism.
> It’s not at all clear to me that 37 single twists around the cylinder
> should count as a single twist. maybe, maybe not.
>
> Even though these sorts of changes will affect the twist counts of
> previous solutions, there is the possibility of adding more twist
> compression logic to MC4D or to a standalone program that will factor
> out any redundancies so that comparisons will always be reasonably fair.
> At the moment I don’t have plans to do any of this work but I think it’s
> great to have these discussions in the hope that we can come up with the
> prefect definitions to base future work on.
>
> -Melinda
>
> matthewsheerin wrote:
> > […] I feel that it’s worth mentioning the old problem in MC4D. A face can be moved to most its possible positions in one move, but the three positions reached by two 90 degree twists require two moves. I’m sure it has been discussed before but a quick look didn’t find it.
>