Message #2105

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Calculating the number of permutation of 2by2by2by2by2 (2^5)
Date: Sun, 06 May 2012 16:18:26 -0700

I feel that it’s not just tricky but it is wrong in most
conceptualizations of the idea of puzzle state spaces. Taking this
natural idea one step further, I would argue that states that have
identical patterns of stickers should be thought of as the same state.
For example, if you scramble any twisty puzzle and then swap all red and
green stickers, then I feel that you still have the same state in terms
of permutations since anything you can say about one version also
applies to the other. For example, twist one face of a Rubik’s cube. For
our purposes, it doesn’t matter which face was twisted. When talking
about that state with each other we will never think to ask about the
particular colors.

Would anyone like to attempt to find the formula for the 3D and 4D cubes
with this extra "color symmetry" constraint?

-Melinda

On 5/6/2012 2:35 PM, Andrew Gould wrote:
>
>
> The choice between 31 and 32 comes down to how you define the
> locations of pieces. If you define all their locations relative to
> one of the pieces it’s 31, but if you define what moves and what
> doesn’t for each twist you can make it 32. I note that for 32, it
> would be tricky to say that rotating the entire puzzle doesn’t change
> the state.
>