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Date: Mon, 11 May 1998 16:48:05 -0400
From: John Bailey
To: Cube-Lovers
Subject: Solving a 4 Dimensional Rubik's type Cube
Announcing a web page at
http://www.frontiernet.net/~jmb184/solution.html which gives the
explicit steps to solve a challenge configuration for a 2x2x2x2 (that's
four dimensions) Rubik type cube.
The challenge configuration is available at
http://www.frontiernet.net/~jmb184/Nteract4.html.
These pages do NOT require a Java enabled browser however, they do
require Netscape 4.0 or Microsoft Explorer 4.0.
This note is to solicit your judgments regarding the difficulty of the 4
Dimensional Rubik with no edge cubes (2x2x2x2.) I believe it is
relatively easy, provided only that the simulation provides for the
cyclic permutation move, (NE-->SW, SW-->NW, NW--->NE)
Background:
Posted on rec.puzzles dl April 21, 1998:
A four dimensional articulated cube is on the web at
http://www.frontiernet.net/~jmb184/4cube.html
The result of marrying a Rubik's cube with a tesseract, this cube is
2x2x2x2. It has 16 corners and 24 faces. It does not have edge cubes
and the corners have no orientation requirement. Only 4 colors are
used. The solution space is thus roughly equivalent to that of a 3x3x3
Rubik if not smaller. It is rendered in Javascript and will run on
Netscape 3.0 and 4.0
This posting caused about 25 hits to the page, but got no follow-up
dialog on the rec.puzzles news dl.
Note that in this first version, the corners are only identified by
color, not by correct position.
I wrote the page without having a clue as to how to solve it. In the
process of just testing code I discovered that it is remarkably
unchallenging, once you get a sense of which corners the various
buttons rotate. (Flipping a glove from left-handed to right-handed can
be done in 4-space, but is impossible in 3-space.) I may not be an
unprejudiced solver, but I would rate the challenge only slightly
harder than a 15 square slider puzzle. To increase the level of
difficulty, a second version of the puzzle was developed. In this
version, the solution requires that the corners are returned to their
correct location. They still do not requires 4-space orientation.
This version was announced in the following posting.
Posted on the rec.puzzles dl May 2, 1998:
A Four dimensional Rubik's Cube with solution.
At http://www.frontiernet.net/~jmb184/Nteract4.html
Re-designed to allow importing of 3D Rubik methods, this version uses
(a slightly extended version of) standard Rubik cube naming of moves
and positions, has a shortcut button for one of the common permutation
moves and a scramble button to provide a challenge position.
I rate the challenge as equivalent to solving two faces of a 3D Rubik
cube. I am looking forward to your comments, opinions, and
suggestions. I am especially interested in positions which cannot be
solved or cannot be solved without extensive permutation moves other
than the one included.
This page has received about 50 hits. But again, there was no
responding dialog on rec.puzzles news dl.
The difficulty of the second version is higher, but I rated the
challenge as equivalent to solving two layers of a 3x3x3 cube. The only
obstacle, an ordinary solver might face, is finding the longish
sequence required to permutate 3 of 4 corners. That's why I provided
the shortcut button (which applies the actions: L'URU'R'LRUR'U' with one
click.)
Discussion:
My concern is that people assume the puzzle is really hard and not worth
the effort. It may be seen as somewhat like the sequences from one
time pads which would be cryptographers who post and ask if anyone can
decrypt them. To make it clear that a solution is not that difficult, I
have now made a page which gives an explicit solution, with
illustrations of each step and even some animation at
http://www.frontiernet.net/~jmb184/solution.html
There are obviously shorter sequences to obtain a solution, however this
one has the value of providing clear checkpoints along the way, such
that a solver can determine if they have missed a twist.
I want and would welcome your judgment about how easy or hard the puzzle
is.
John Bailey
jmb184@frontiernet.net
http://www.frontiernet.net/~jmb184
May 11, 1998