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'Cubic Net' printed from http://nrich.maths.org/
Although it is very difficult to solve the Cubic Net fully, it is
good fun to play with for all ability ranges and a source of many
As a whole class activity teachers may like to try the following
Choose a sequence of moves, such
as PRP or WWGGB, on a reset net
Before doing the moves, ask questions such as:
- Can you choose a corner or edge square on the net which you
know will not move?
- Choose a square on the net. What colour will it turn into?
- What sequence of moves will undo the original sequence?
- How many squares on the net will change colour overall?
Scramble the net with 1, 2 or 3
- Ask students to discuss how to
unscramble the net.
- Ask for volunteers to try to
unscramble the net. You can press the Restore Last Scramble button to allow
others to have a try.
- Since the faces only move
anti-clockwise you may like to discuss with the class the discovery
that a 1 move scramble takes 3 twists to undo and so on.
Secretly record and play a move
sequence of between 1 a 5 moves using the 'Record moves to
- Ask students to guess how many moves
they think that the net has been scrambled by
- You can play the sequence of moves so
that students can count and see the moves in action
- Once the sequence of moves is known
to the class reset the net. Choose a square on the net which you
know will move. Ask the class to visualise the motion of this
square throughout the move sequence, making notes if they wish.
Play the move sequence asking the class to follow the path of their
chosen square. Who correctly predicted the end location?
Black out the corner or edge
Ask the students to focus on a particular corner. Tell them
that you are going to make a series of moves and that they need to
try to follow the path of that square in their head.
Other discussion points
- Make the moves. Ask for two volunteers to describe their
predictions. This should create a discussion about effective ways
to describe the squares on the net, such a Red face (2, 1) for
second row and first column on the red face.
- Once a labellelling system is in place the whole class can
play. They write their predictions down and swap with a a partner.
Those who make mistakes are eliminated.
- Although many people can solve a Rubik's cube from a given
position, the problem of the Rubik's cube has not yet been fully
understoodby mathematicians due to its enormous complexity.
- Mathematicians are still actively working on the main problem
which is: what is the smallest number of moves with which you can
guarantee to solve any Rubiks cube configuration?
- It has very recently been shown that 26 moves is sufficient to
solve any Rubik's cube configuration (see here for a
news report on this achievement)
There are many web sites devoted to the Rubik's cube problem. The
site solution page
is a good place for the interested to find
more information.Why not set an investigative homework on the
properties of the Rubik's cube.