Newsgroups: rec.puzzles
From: hoey@aic.nrl.navy.mil (Dan Hoey)
Date: 25 Oct 1994 23:06:07 GMT
Subject: Re: Rubik's Cube impossible states

chris.pel...@octel.com writes (in entirety):

> Dan Hoey writes:

> >Well, you seem to have a vaguely correct idea of this, but the details
> >of your list are somewhat confused.  First they are called "orbits", ...
> >You mean "e.g.", not "i.e."--there are a lot of ways to place the

> I stand corrected!  Sheesh...

I must protest the dishonesty of your editing my reply to suggest
that I discussed only these trivial errors in your description of the
impossible states of Rubik's Cube.  Your rudeness in following up with
an article that has nothing to say about puzzles speaks for itself.

As for the ObPuzzles I posed:

  How many ways can you place the stickers so that the cube is not
  solvable?

  How many of them have a piece with a pair of opposite colors
  adjacent?

  How many have duplicate pieces?

I think these may be quite challenging questions.  The first is easily
seen to be 54!/(9!)^6 - 6! 8! 12! 2^10 3^7, if we ignore the position
of the cube in space.  But figuring out how many ways there are if we
ignore whole-cube moves is a neat problem.  The others are quite
difficult even ignoring symmetry.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil