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.
A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Use the Thesaurus if you don't
know how to find the subsets of a given set.
In counting the tours remember that you can start from any vertex. From
the start there are 3 possible ways to go and at the next vertex two
ways to go.
Can you label the vertices of a cube with the subsets of the given set
so that an edge connects two vertices if it is possible to move from one
subset to another in the sequence?