# 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

>

>