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Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2