# 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