We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Solving the Net
Stage: 5 Challenge Level:
Although there are many algorithms for operating on a Rubik's cube,
there is no one 'method of solution'. Making a face and the first
layer is generally considered straight forward and can be done
directly by inspecting the configuration of the cube (and, hence,
Completing the second layer is more difficult and is best broken
down into routines which flip individual squares on the cube.
A common way to proceed is to note that there are series of
operations which permute a subset of the middle edges, leaving the
other middle edges in the same place. By using combinations and
variations of these operations in turn it is possible to create a
net with all of the middle edges in place. The next step is to
realise that there are series of operations which permute the
corners of the net only, leaving all of the middle edges in place.
By using combinations and variations of these operations on the net
with all of the middle edges in place, it is possible to finish off
the net in its entirety.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.