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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

The use of set terminology here should not hold anyone up as they can find the definition in the Thesaurus. This is an exercise in combinatorics and it also gives a method for solving the problem about the sequence of subsets.