Message #4153

From: Luna Harran <scarecrowfish@gmail.com>
Subject: Re: [MC4D] Non-associative "twisty" puzzles
Date: Mon, 01 Oct 2018 01:02:29 +0100

That’s interesting. Adding i*h and j*h felt more natural though, and makes
shorter solutions, I’d presume. I wonder if adding i*j*h would make it even
shorter, and what the smallest moveset with a certain God’s number is. It’s
6 for (i, j, h, i*h, j*h), but is there a set of five (or less) moves for
which God’s number is less than 6?

What I meant was, the puzzle formed from (i, j, h, i*h, j*h) ONLY is
associative, as you can no longer compose the moves, only apply them
sequentially. Therefore, you can solve it without worrying about
associativity.

~Luna

On Mon, 1 Oct 2018, 00:32 mananself@gmail.com [4D_Cubing], <
4D_Cubing@yahoogroups.com> wrote:

>
>
> I find that you only need to expand the generators by one, adding only
> (i*h) to {i, j, h}, and you can rely on individual generators in every step
> to solve the puzzle. The space of the puzzle is only 240 after all.
>
> I think of such prepared expressions like this as "macros". We can rely on
> native generators and macros in each step to solve the puzzle. I think if
> we have a larger non-associative puzzle, we need to prepare more "macros".
> But I don’t think macros removes the non-associativity of the puzzle.
>
> Nan
>
>