Message #2119

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Calculating the number of permutation of 2by2by2by2by2 (2^5)
Date: Mon, 07 May 2012 14:47:56 -0500

On Sun, May 6, 2012 at 9:45 PM, Brandon Enright wrote:

> There are some puzzles that can be solved into their mirror color
> scheme (such as the Dino Cube) and some puzzles that can be solved into
> any permutation of their colors such as the Big Chop (and Little
> Chop). In the case where a puzzle can be solved into the mirror state
> you’d divide by 2 and in the case where all permutations of colors are
> available it would be #colors!. I’m sure there are puzzles that can
> only be solved into an even permutation of the colors so those would be
> #colors! / 2.
>

cool! I didn’t know that, so thanks for sharing :)

In dividing by these numbers, are you calling these different pristine
positions "the same", just like we call a solution to the Rubik’s Cube the
same when you reorient the whole puzzle by 90 degrees? To me, a mirroring
(or other permutation) of the coloring scheme feels like a fundamentally
different state, because you must do some twisting to get from one of these
pristine states to another.

Intriguing stuff!
Roice