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Peter sent us this solution, using the starting point we gave:
There are 6 vertices and 5 edges. Let's suppose the magic constant is S and this is the same at each vertex. The total of all the numbers 1 + 2 + ... + 11 = 66 but the numbers on the edges, a,b,c,d,e are counted twice. So, adding the magic sum at all six vertices:
(a+b+c+d+e)+66=6S
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.