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 this plum tree graph to make it totally magic!
The numbers on the edges are counted twice.
The reasoning needed here is much the same as for the problem Plum Tree. See the detailed hint for Plum Tree.