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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.
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.