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This problem is now part of the collection Magic Letters.
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.
Explore some of the different types of network, and prove a result about network trees.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.