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This problem follows on from 9 Weights
You have twelve weights, one of which is heavier or lighter than the rest, but you don't know which one is heavier or lighter, and a balance. Using just 3 weighings on the balance, can you find a way to identify which weight is the odd one out, and whether it is heavier or lighter?
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.