Thread: "Scientific American article on Rubik's cube and groups"

Hi there,

Just came across this article and thought it might be of interest to those =
of you for whom 3D Rubik's cube-style puzzles have become way too easy (I'm=
guessing that applies to most of you)

http://www.scientificamerican.com/article.cfm?id=3Dsimple-groups-at-play

Have fun,

Jonathan

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I saw this at www.mathpuzzle.com:

*Void Cube and other Variants* The 2007 winner of the Nob Yoshigahara
Puzzle Design Competition was the Void
Cube(youtube), by
Katsuhiko Okamoto. These are now available at
gentosha-edu.co.jp .
Easier to order are some of the exotics now available at mefferts.com.
The mirror
block (yousaytoo)
is another variant.

These are pretty neat looking, and it would be relatively easy to make code
changes for analogues... simply don't draw 1C pieces, and alter the function
which checks for a solved puzzle accordingly. Anyone want to comment on how
this affects the difficulty or number of reachable positions?

One random thing I could quickly observe is that number of checkerboard
patterns on MC4D is extended for the void cube. As a specific
example, an 8-cycle
version of the checkerboardis
now possible (in that picture, one of course needs to ignore the 1C
pieces).

Some more questions I'd be interested to hear thoughts on: Could you have a
physically stable 4D void cube version with no 1C pieces and no 2C pieces?
I think the answer might be yes. And if so, do stable n-dimensional void
cubes only need two piece types in general?

Take Care,
Roice

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Void Cube and other Variants=20

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as the blank">Void Cube (youtube), by Katsuhiko Okamoto. These are now availab=
le at =3D"_blank">gentosha-edu.co.jp. Easier to order are some of the exotics=
now available at meffer=
ts.com. The -rubik-s-cube/11386" target=3D"_blank">mirror block (yousaytoo) is anot=
her variant.

Thanks for sharing this article. I actually have a few puzzles that
more or less follow these principles. Perhaps the best example is
"Triple Cross", which you can see a picture of here:

http://www.passionforpuzzles.com/puzzles/triplecross.php

You can also make the regular 3D Rubik's cube a little more like these
by restricting yourself to only twisting certain faces. For example,
scrambling and then solving regular Rubik's cube by only twisting two
adjacent faces is much harder then solving it normally.

It might be interesting to play with the 4D version of the puzzle in
that way, something that had never occurred to me. I bet randomizing
and solving the 4D puzzle by twisting only two or three adjacent
"faces" would be harder than or at least very different from solving
the puzzle in the normal way.

--Jay