Age 16 to 18 Challenge Level:
For the first part of this problem try to view the cubes from above
to turn it into a simpler 2D problem to begin with.
The second part of this problem will be greatly simplfied if you
work with a physical model of a cube, preferably wire framed which
you can see through (such as with polydron) and the bigger the
better. You may wish to attempt to create frames using wires or
straws to help to understand the problem.
Instead of trying to visualise the entire solid 3 dimensional cube,
you may like to consider the cube as defined by its 8 corners. If
you work out where the corners go then the rest of the cube will
follow by joining up with straight lines and planes.Visualising the
objects by looking directly at one of the original faces will help
you to understand the problem.
Finally, don't forget that if you can work out the view of the
interpenetrated object in the direction of one of the faces, then
the view in the direction of the other faces may follow by