Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Faisal from Arnold House School offered a strategy for working on this problem:
We had several more good solutions for the first part of this problem from pupils at Highcliffe Primary School. Whitney and Joe said:
Sam and John explained that the length of the locus ...