From ccw@eql.caltech.edu Fri Nov 1 19:10:26 1991
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Date: Fri, 1 Nov 91 15:49:59 PST
From: ccw@eql.caltech.edu (Chris Worrell)
Message-Id: <911101154959.23403c64@EQL.Caltech.Edu>
Subject: What is the smallest cube which has all possible types of pieces?
To: cube-lovers@ai.mit.edu
Some cube discussion has started in rec.games.misc. I am trying to
re-direct it to rec.puzzles, or hopefully cube-lovers.
This is a copy of what I posted to rec.games.misc and rec.puzzles.
Message follows:
------------------------------------
Newsgroups: rec.games.misc, rec.puzzles
Subject: Re: Rubik's Wonderful Madness
Followups-to: rec.puzzles
johnf@apollo.hp.com (John Francis) writes...
>
>The 5x5x5 cube is the largest "interesting" cube from a solvers viewpoint.
>The corner cubelets of cubes of all sizes can be solved the same way.
>Similarly with the edge-centre cubelets of odd-sized cubes, etc., etc.
>The 5x5x5 does not actually require any new solving techniques (if you can
>solve a 3x3x3 and a 4x4x4 you can solve a 5x5x5), but it is the smallest
>cube that contains cubelets of all possible types.
Actually the 7x7x7 has a type of piece that the 5x5x5 does not have.
This is a "face" piece which is not on a main diagonal of the face, nor
on the main horizontal or vertical. These pieces come in 2 flavors,
right-handed and left-handed (but I am not sure which should be called which).
----------------------
|A |B |C |D | | | | The 2x2x2 has types A
---------------------- The 3x3x3 has types A, D, K
| |E |F |G | | | | The 4x4x4 has types A, B(C), E(I)
---------------------- The 5x5x5 has types A, B(C), D, E(I), G(J), K
| |H |I |J | | | | The 6x6x6 has types A, B, C, E, F, H, I
---------------------- The 7x7x7 has types A-K
| | | |K | | | |
---------------------- B and C are distinct at size 6+, but the same
| | | | | | | | sorts of procedures work on both.
---------------------- Similarly for E & I.
| | | | | | | | Similarly for G & J. For odd sizes 7+.
---------------------- Similarly for H & F. These are related
| | | | | | | | by mirror imaging. Not by slice renumbering,
---------------------- like the above.
Types F & H only start appearing at size 6. There are 24 of each of these
pieces, and a type F can not be mixed with a type H.
Discussions about the Rubik's cube and related puzzles should probably be
directed to rec.puzzles rather than rec.games.misc.
There is also a mailing list for theses topics.
cube-lovers@ai.mit.edu
Send mail to cube-lovers-request@ai.mit.edu to be added.
Some sites may also see this as a newsgroup mlist.cube-lovers. But do not
post to this group.