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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!

Cube Net

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
How many tours that visit each vertex once and only once can be traced along the edges of a cube? How many of these tours can return to the starting point thus completing a Hamiltonian Circuit?

How many different ways can the subsets of the set $\{a, b, c\}$ be arranged in a sequence so that each subset differs from the one before it by having exactly one element inserted or deleted?