What is Rubik's Cube?
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......

Rubik's Cube is a cube shaped puzzle.
At first glance it consists of 27 cubelets, which make
together a 3x3x3cube. 
...... 
In reality there are 21 pieces: 1 main piece with three
axles, 8 corner pieces (corner cubelets) with three colours and 12 edge
pieces (edge cubelets) with two colours. 

The colours of my cube are white/yellow, orange/red (here:
orange=pink) and green/blue. After several random turns the cube is coloured.
If the cube is solved, every lateral face has the same colour.
The main problem is solving the cube ;). 
Solution of the SPIEGEL Magazine
slightly altered
Introductory
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Ernö Rubik, a Hungarian professor of physics and
design, invented the cube in 1974. About 1980 Rubik's cube spread out all
over the world like a virus. In the early 80's about 100 million cubes
were sold worldwide. People tried to solve it. But most of them kept to
one slice or to two slices.
In Germany the magazine DER SPIEGEL published the first
solution, which you could understand. This solution is still of topical
interest.
The copyright is at the SPIEGEL and the journalist Albrecht
Kunkel.
The following seven pictures show how the cube is solved.
(Picture 4 und picture 6 may be different.)

The turns of the slices are shown by a 3x3 square and
an arrow. The squares are always the front squares, the arrow describes
a quarter turn in direction of the arrowhead. The arrows are in the slice
you must turn.
The illustration opposite shows the meaning of the squares
with arrows in two examples. 

This is more practical.
. 
Remember one principle at the following
seven steps of this solution:
Never turn the cube itself but
only separate slices during the sequences of turning. That means the orientation
of the cube in space is always the same while turning.
Building the
First
Slice top
Solving the first and middle slice you have to hold the
cube so that the white centre of the face is at the top.
1st step: Solving the edge cubelets.
You look for the edge cubelet blue/white and rotate it
to front/down/middle.
There are two possibilities 1a) or 1b).
1a) white underneath
1b) white in front
You repeat the moves with the orange, the green and the red
faces in the same way.
Result: On the top there is a white cross. The colours
of the edge cubelets and the centre of the four faces have the same colour.
(Picture 1 of 7)
2nd step: Solving the corner cubelets.
There are four corner cubelets with the colour white.
You hold the cube so that white is at the top and blue in front.
E.g. you have to move the corner cubelet white/red/blue
to its correct position front/right/top.
First you move this cubelet to the place front/down/left.
There are three possibilities 2a), 2b) or 2c).
2a) white left
2b) white in front
2c) white underneath
In the same way you deal with the three remaining white corner
cubelets.
Result: The top slice is completely white. The colours
of the edge cubelets match the centre cubelets.
Building the
Middle Slice top
3rd step
In the middle slice move only four edge cubelets blue/orange,
blue/red, green/orange and green/red. You must do this by starting at the
bottom. You hold the cube so that white is at the top.
You have to turn the down slice so that one of the edge
cubelets blue/orange or blue/red is at front/down/middle. There are two
possibilities 3a) or 3b).
3a) to the right
3b) to the left
If the blue square shows underneath, you start with another
colour.
If all cubelets are in the middle slice, move the cubelet
down to the middle by one of the sequences 3a) or 3b) first.
Result: The top slice and the middle slice are in the
right positions.
Building the
last Slice top
You turn the cube to solve the last slice (white underneath,
yellow at the top).
4th step: Switch the position of two cubelets.
You turn one of the four edge cubelets yellow/blue, yellow/orange,
yellow/green, yellow/red to the face with the correct colour (if yellow
is not at the top, don't worry!). If the remaining cubelets are not
at the correct positions, you have to switch them over the left edge cubelet
at the top. Probably you will have to repeat this sequence. (Picture
4 of 7)
5th step: Flip the edge cubelets
Though all edge cubelets are in the correct position,
they might be wrong. Yellow is not at the top.
You have to flip them. You hold the cube so that the
edge
cubelet is right/top/middle. Now there are eight moves.
If the cube is coloured after these 8 turns, go further.
Turn the next edge cubelet to be flipped to the same place right/top by
turning the whole slice (Don't turn the whole cube). Then there are the
eight moves again.
Result: There is a yellow cross. You turn the top slice
so that the edge cubelets are at the correct places.
6th step: Switch the positions of three corner
cubelets
First you move the four remaining corner cubelets to
the proper positions. Their colours needn't be correct.
If all four corner cubelets are in the proper position,
then the following sequence is unnecessary.
If all the four corner cubelets are at a wrong place
after aligning , then there are a further 22 moves:
If all the four corner cubelets are still in the wrong places,
you have to repeat the eight moves. The front face must stay in front.
After these moves one corner cubelet is in a proper place.
Turn the cube so that this corner cubelet is back/left. Now you repeat
the eight moves.
Result: The four corner cubelets are in their correct places.
Comments to the 6th step
Short after publishing (4/1981) there appeared
a solution for the problem "switching the position of three corner cubelets",
which I describe now. You only need 8 moves instead of 22.
Ich tell this abbreviation conditionally.
7th step: Rotating the corner cubelets.
The colours of a corner cubelet have to turn.
You hold the cube so that a corner cubelet is top/right/front.
Then there are eight moves.
If yellow is not at the top of this special corner cubelet,
you repeat these eight moves.
Then you turn the top slice (not the whole cube), so
that the next corner cubelet is top/right/front.
You repeat the 8 or 2x8 moves.
If all the four corner cubelets are rotated, yellow must
be on the top. Now there is a last step. Turn the last slice. The six faces
have one colour. FINISHED!
Planned
Chaos
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Is it possible to turn a cube so
that you have every colour on each face at least once? Yes it is.
(Start with blue at the front,
white at the top)
Taking
to Pieces top
You can also solve the cube by
taking it apart and putting it together.
There are some products with a
screw at the centre of a face. You can unscrew it. Then you can solve the
cube.
You can take apart most products
only with a little force. You turn the top slice about an angle of 45 degrees.
You lift the top slice with a screwdriver or a spoonhandle carefully.
In this position you can remove an edge cubelet and then the adjacent corner
cubelets.
If you are very clever you solve the cube by removing
the adhesive films and sticking them again ;).
Solving
with a StopWatch top
Those who can solve the cube see
the next challenge: Solving the cube as quickly as possible.
The times solving the cube are
different. It depends on the arrangement of the cubelets at the beginning.
But there are average times.
The professional cube turners need
no more then 90 moves. They know a lot of sequences to enable react them
to special situations appropriately. They don't solve the cube step by
step. They see many cubelets together.
Besides they use silicone oil.
In the "Guiness Buch der Rekorde
1986" you find:
On June 5, 1982 Min Thai,
USA, won the Rubik`s Cube Championship in Budapest. His time: 22.95
s.
Solving
the Cube with Little Numbers of Sequences top
Most of the people prefer a method
with a small number of sequences (not moves). If you solve the cube you
are not willing to look at a paper, you solve it by heart.
In this respect the SPIEGEL solution
is a good one.
If you have some practice you can
order the first slice easily. Step 2c) is not necessary, you can use 2a)
and 2b). You need only sequences of no more than eight moves.
Nevertheless you need 120 to 180
moves, because you have to repeat sequences again and again. If you have
bad luck you need 75 moves for the last step "Rotating the corner cubelet".
The cube can be solved with the Spiegel method in 2 to 3 minutes.
Some
Mathematics
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In the book of Trajber (3) there
is a mathematical theory of the cube.
You number the squares, which you can move, from 1 to
48 (48 = 6x96). A move or a sequence of moves brings you to a new arrangement
of the numbers 1 to 48. This is called a "permutation". All the permutations
form a "group".
So instead of looking into Rubik's Cube you can occupy
yourself with the group.
One interesting point in the theory of groups is transferred
to the cube:
If you repeat a move or a sequence of moves, you always
come back to the beginning.
If you would like to have some exercise with the sequences
of the SPIEGEL solution, you do it like this:
...... 
You take the solved cube and follow one sequence of moves
again and again. After n steps you come back to the
clear cube.
n is at the second column. 
Theoretically there are 54!/(9!*9!*9!*9!*9!*9!) = 1.10*10^38
combinations of 54 squares of a 3x3x3 cube.
Rubik's cube shows "only" 8!*3^8*12!*2^12 = 519,024,039,293,878,272,000
=5.19*10^20 combinations of the 54 squares, if you take apart the cube
and put it together.
43,252,003,274,489,856,000 combinations (1/12) appear
at the cube while turning.
Patterns
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A wide field of activities is finding new patterns.
Here is an example, which you can develop to find more
patterns. (Each arrow means a quarter turn.)
If you repeat the sequence, you return to the solved cube.
Variations:
...... 
If you don't start with the solved cube, but with one
variant at the left, you get new patterns. 

If you turn the slices in another way, you get new patterns,
too. 
You get 12 patterns:
Rubik's
Cube on the Internet top
German
Lars Petrus
Rubiks
Zauberwürfel auf Zeit lösen
Michael Jasmund
Zauberwürfel
(Lösung, Spiel, Modelle)
Oliver Reimann
Anleitung
für den Zauberwürfel
RekordKlub Saxonia
Rubik's
Cube
Ronald Bieber
Rubiks
Cube
Sigrun Deweß
RubikZauberwürfel
ordnen
SpiegelWissen
Schrei
Hurra! Schmeiß 'ne Runde!
Die Spiegelausgabe 4/1981 vom
19.01.1981 ist jetzt (Feb2008) für den privaten Gebrauch freigegeben!
:)
Urs Manser
Rubik's
Cube (Lösung)
Wikipedia
Zauberwürfel
English
Georges HELM
Collection
of Rubik's cubes and related puzzles
Jaap Scherphuis
Rubik's
Cube 3x3x3, Barrel/Octagon
Jessica Fridrich
My
speed cubing page
Lars Petrus
Solving Rubik's Cube
for speed
Nader (naderc)
CV
Rubik  Computer sees Rubik's cube and solves it (The Spiegel solution
as a video)
Rubik
online
Ernö Rubik's Official Homepage
Stefan Pochmann
Stefan
Pochmann's Cube Corner
Wikipedia
Rubik's
Cube
References (German) top
(1) DER SPIEGEL Nr.4/1981
(2) Josef Trajber: Der Würfel, Niedernhausen/Ts.
1981 (Falkenverlag 0565)
(3) Josef Trajber: Der Würfel für Fortgeschrittene,
Niedernhausen/Ts. 1981 (Falkenverlag 0590)
(4) Tom Werneck: Der Zauberwürfel, München
1982 (Heyne 4831)
(5) Tom Werneck: Der Zauberwürfel für Könner,
München 1982 (Heyne 4834)
(6) Kurt Endl: Rubik's Rätsel des Jahrhunderts,
Giessen 1981
(7) Alexander H.Frey, Jr and David Singmaster: Handbook
of Cubik Math, Hillside New Jersey1982 [ISBN 0894900609]
Feedback: Email address on my main page
This
page is also available in German.
URL of
my Homepage:
http://www.mathematischebasteleien.de/
©
1999 Jürgen Köller
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