# Rubik's Cube - www.maths.nott.ac by wulinqing

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```									       Day of Exploration
25th April 2009

Solving the
Rubik’s Cube
Rubik’s Trivia

Who invented the Rubik’s cube?

Erno Rubik
Rubik’s Trivia

How old was the youngest person to
solve a Rubik’s cube?

4 years 6 months and 10 days
Rubik’s Trivia

What’s the least amount of moves
needed to solve a 3x3 Rubik’s cube
from it’s ‘hardest’ scrambled state?

25 moves
Rubik’s Trivia

In it’s height of popularity, between
1980 and 1983, how many Rubik’s
cubes were sold worldwide?

100 million
Rubik’s Trivia

What time is the current world record
for solving a 3x3 Rubik’s Cube?

7.09 seconds
Rubik’s Trivia

That means that to solve a Rubik’s
Cube efficiently and quickly requires
....

3.5 moves per second!!!
Rubik’s Trivia
Rubik’s Solving
Thinking logically...

There are 43,252,003,274,489,856,000
configurations on the Rubik’s cube.

12 edges      (12! • 212)(8! • 38)   8 corners

2•2•3
Rubik’s Solving
43,252,003,274,489,856,000

• If one were to make one move every second, it
would take 1,370,000,000,000 (1.37 trillion) years
to reach every case, assuming no repeats
• That amount of time spans the age of the
universe ten times
Rubik’s Solving

What strategy do we need to take to
solve the Rubik’s cube?

Let’s play!
Rubik’s Solving
Thinking logically...

20 unique pieces NOT 54 stickered squares.
Rubik’s Solving
Thinking logically...
The centers are fixed on a central mechanism, so
they don’t move relative to each other
Rubik’s Solving
Thinking logically...
The colour of a center determines what colour
that face will be when the cube is completed
Rubik’s Solving
What you will learn:

To solve the Rubik’s cube we need to use a
special algorithm.
With practice this method can be used to solve
any cube in 3 to 4 minutes.
Rubik’s Solving

6-stage sequence
Rubik’s Solving
There are 3 sorts of pieces
Face-centres
Edges
Corners
Rubik’s Solving
Rubik’s Solving
Rubik’s Solving
Rubik’s Solving
Rubik’s Solving
Stage 1: Forming the Cross
• The first stage of the solution is to form a cross like in the
diagram below.

• In this diagram, only the cubes we are interested in are
coloured, the remainder are shaded grey.
Rubik’s Solving
Stage 1: Forming the Cross
• There are two main steps to reach this point,
the first makes the cross in the first layer, the
second extends the cross to the centre
squares of the middle layer.
• Forming the top cross
• Extending the cross
Rubik’s Solving
Stage 1: Forming the Cross
• Forming the top cross
Firstly move your cube so that the centre yellow
square is at the top of your cube.
Rubik’s Solving
Stage 1: Forming the Cross
• Forming the top cross
Once you have done this, the next step is to form a
cross on the top.
Rubik’s Solving
Stage 1: Forming the Cross
• Forming the top cross
Or the yellow cube may need to be moved in this way:
Rubik’s Solving
Stage 1: Forming the Cross
• Forming the top cross
Or the yellow cube may need to be moved in this way:
Rubik’s Solving
Stage 1: Forming the Cross
• Forming the top cross
You should now be at this point:
Rubik’s Solving
Stage 1: Forming the Cross
• Extending the top cross
We now want to extend the cross to look like:
Rubik’s Solving
Stage 1: Forming the Cross
• Extending the cross
Change over 2 neighbouring edges
Rubik’s Solving
Stage 1: Forming the Cross
• Extending the cross
Change over 2 opposite edges
Rubik’s Solving
Stage 2: Finishing the Top Layer
• The second step completes the top layer by
inserting the top corners
Rubik’s Solving
Stage 2: Finishing the Top Layer
• Step A
Find a corner piece in the bottom layer that should be in
the top layer. Turn the bottom layer so that that piece is
direct below its home in the top layer.
Rubik’s Solving
Stage 2: Finishing the Top Layer
• Step B                         If you find that the corner
piece is not the correct way
round
– then do this twice more

If still not correct do it twice
more !!!
Rubik’s Solving
Stage 3: Completing the middle Layer
We should now be at this point:
Rubik’s Solving
Stage 3: Completing the middle Layer
Our next challenge is to complete the middle:
Rubik’s Solving
Stage 3: Completing the middle Layer
Rubik’s Solving
Stage 3: Completing the middle Layer
Keep swapping corner
cubes until you complete
the middle layer
Rubik’s Solving
Stage 4: Forming the bottom cross
We should now be at this point:
Rubik’s Solving
Stage 4: Forming the bottom cross
Flip the cube upside down:   We are going to make
another cross:
Rubik’s Solving
Stage 4: Forming the bottom cross
Turn the cube until you get one of these arrangements:

Keep repeating the
sequence of moves
Rubik’s Solving
Stage 5: Moving the bottom edges
Turn the top face and the whole cube until either all four
edges are correct, or else exactly one edge is correct
(in this case red) and is in the position shown.

Repeat sequence of
Rubik’s Solving
Stage 6: Moving the bottom corners
Turn the cube until any corner      Repeat this process until
piece is in the correct position:   all corners are correctly placed:
Rubik’s Solving
Stage 6: Moving the bottom corners
Then take one corner and use the process (x2 or x4):

Then turn the TOP LAYER only
until the next corner is at the front.
Repeat x2 or x4 on each corner
Rubik’s Solving
Stage 6: Moving the bottom corners
After applying the process four times you should get:

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