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.
Plane to See
Age 16 to 18 Challenge Level
In the cube illustrated the point $P$ is the midpoint of $AB$
and the point $Q$ is one quarter of the way along the edge
The plane through $PDQ$ cuts the cube into two. Find the ratio
of the volumes of the two pieces.
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.