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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.

Magic Caterpillars

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

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.