Date: Fri, 01 Nov 91 15:49:59 -0700 (PST)
~~~ From: Chris Worrell <ccw@eql.caltech.edu >
~~~ Subject: What is the smallest cube which has all possible types of pieces?

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
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
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