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Instant Insanity

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.

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Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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Plum Tree

Label this plum tree graph to make it totally magic!

The Great Weights Puzzle

Age 14 to 16 Challenge Level:
This problem puts emphasis on trying to gain as much information as possible from each weighing, whatever the outcome. So if a weighing has one outcome which gives you a lot of information, but another outcome which doesn't gives you much new information, it is probably not going to be a useful way of identifying the odd weight.